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xsqrt(x^2-1)+ln|x+sqrt(x^2-1)|
Derivada de la función/ xsqrt(x^2-1)+ln|x+sqrt(x^2-1)|

Derivada de xsqrt(x^2-1)+ln|x+sqrt(x^2-1)|

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     ________      /|       ________|\
    /  2           ||      /  2     ||
x*\/  x  - 1  + log\|x + \/  x  - 1 |/
xx2−1+log⁡(∣x+x2−1∣)x \sqrt{x^{2} - 1} + \log{\left(\left|{x + \sqrt{x^{2} - 1}}\right| \right)} 
x*sqrt(x^2 - 1) + log(Abs(x + sqrt(x^2 - 1)))
Gráfica
02468-8-6-4-2-1010-200200
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                            //         /     /         2\\              \                                                                                             \                       
                            ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                       
                            ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |     /       _________\
                            ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|     |      /       2 |
                            ||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*sign\x + \/  -1 + x  /
                            ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                       
                            ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                       
                            ||                /     -1 + x              |                                                                                             |                       
                            ||               /   -------------          |                                                                                             |                       
   ________         2       ||              /        /      2\          |                                                                                             |                       
  /  2             x        \\            \/     sign\-1 + x /          /                                                                                             /                       
\/  x  - 1  + ----------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------
                 ________                                                                  /       _________\ |       ________|                                                               
                /  2                                                                       |      /       2 | |      /  2     |                                                               
              \/  x  - 1                                                                   \x + \/  -1 + x  /*|x + \/  x  - 1 |
x2x2−1+x2−1+(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))sign⁡(x+x2−1)(x+x2−1)∣x+x2−1∣\frac{x^{2}}{\sqrt{x^{2} - 1}} + \sqrt{x^{2} - 1} + \frac{\left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right) \left|{x + \sqrt{x^{2} - 1}}\right|}
Simplificar
Segunda derivada [src] 
                                                                                                                                                                                                         /                                                                                                                                                                                                                                                                                          /                              /       /      2\           /      2\\                              \                       \                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                         |                                                                                                                                                                                                                                                                                          |                            2 |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\                |                       |                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                         |                                                                                     /             _______________                                                              \                                                      /          _______________                       \ |                           x *|-1 + -------------------------------|*sign\-1 + x /                |                       |                                                                                                                                                                                                                                                                                                                                                                                      
                                                                                                                                                                                                         |                                                                                     |            /          2     /       /      2\           /      2\\    /     /         2\\|                                                      |         /          2        /     /         2\\| |                              |                  /      2\         |                              |    /     /         2\\|                                                                                                                                                                     2                                                                                                                                                                                                                
                                //         /     /         2\\              \                                                                                             \                              |                                        /         /     /         2\\              \ |           /     -1 + x      |     2*\-1 + x /*DiracDelta\-1 + x /|    |atan2\0, -1 + x /||                                                      |        /     -1 + x         |atan2\0, -1 + x /|| |   2           /      2\      \              sign\-1 + x /         /                     /      2\|    |atan2\0, -1 + x /||                          //         /     /         2\\              \                                                                                             \                                               //         /     /         2\\              \                                                                                             \                       
                                ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                              |                                        |         |atan2\0, -1 + x /|     /      2\| |     x*   /   ------------- *|-1 + -------------------------------|*cos|-----------------||                                                      |x +    /   ------------- *cos|-----------------||*|4*x *DiracDelta\-1 + x / + ------------------------------------------------------- + sign\-1 + x /|*cos|-----------------||                          ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                                               ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                       
                                ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |   /    /       _________\\   |    /     /         2\\                 |    x*cos|-----------------|*sign\-1 + x /| |         /        /      2\  |                  /      2\         |    \        2        /|            /     /         2\\                       |      /        /      2\     \        2        /| |                                                         2                                        |    \        2        /|     /       _________\   ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |       /       _________\                      ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |     /       _________\
                                ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\| d |    |      /       2 ||   |   2|atan2\0, -1 + x /|     /      2\   |         \        2        /              | |       \/     sign\-1 + x /  \              sign\-1 + x /         /                       |      2    2|atan2\0, -1 + x /|           /      2\   \    \/     sign\-1 + x /                        / \                                                   -1 + x                                         /                       |     |      /       2 |   ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|      2|      /       2 |   /         x      \ ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|     |      /       2 |
                                ||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*--\sign\x + \/  -1 + x  //   |sin |-----------------|*sign\-1 + x / - |1 + --------------------------------------|*|-1 + -------------------------------------------------------------------------------------| + 4*x *sin |-----------------|*DiracDelta\-1 + x / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/  -1 + x  /   ||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /| *sign \x + \/  -1 + x  /   |1 + ------------|*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*sign\x + \/  -1 + x  /
                                ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              | dx                           |    \        2        /                 |                  _______________         | |                                                  2                                       |            \        2        /                                                                                                         _______________                                                                             |                          ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                            |       _________| ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                       
                                ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                              |                                        |                 /          2             | \                                            -1 + x                                        /                                                                                                                                       /          2                                                                                 |                          ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                            |      /       2 | ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                       
                                ||                /     -1 + x              |                                                                                             |                              |                                        |                /     -1 + x              |                                                                                                                                                                                                                                   /     -1 + x                                                                                  |                          ||                /     -1 + x              |                                                                                             |                            \    \/  -1 + x  / ||                /     -1 + x              |                                                                                             |                       
                                ||               /   -------------          |                                                                                             |                              |                                        |               /   -------------          |                                                                                                                                                                                                                                  /   -------------                                                                              |                          ||               /   -------------          |                                                                                             |                                               ||               /   -------------          |                                                                                             |                       
        3                       ||              /        /      2\          |                                                                                             |                              |                                        |              /        /      2\          |                                                                                                                                                                                                                                 /        /      2\                                                                              |                          ||              /        /      2\          |                                                                                             |                                               ||              /        /      2\          |                                                                                             |                       
       x             3*x        \\            \/     sign\-1 + x /          /                                                                                             /                              \                                        \            \/     sign\-1 + x /          /                                                                                                                                                                                                                               \/     sign\-1 + x /                                                                              /                          \\            \/     sign\-1 + x /          /                                                                                             /                                               \\            \/     sign\-1 + x /          /                                                                                             /                       
- ------------ + ------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
           3/2      _________                                                                   /       _________\ |       _________|                                                                                                                                                                                                                                                                        /       _________\ |       _________|                                                                                                                                                                                                                                                                                        2                   2                                                                                                                                                            2                                                                                          
  /      2\        /       2                                                                    |      /       2 | |      /       2 |                                                                                                                                                                                                                                                                        |      /       2 | |      /       2 |                                                                                                                                                                                                                                                                      /       _________\  |       _________|                                                                                                                                           /       _________\  |       _________|                                                                       
  \-1 + x /      \/  -1 + x                                                                     \x + \/  -1 + x  /*|x + \/  -1 + x  |                                                                                                                                                                                                                                                                        \x + \/  -1 + x  /*|x + \/  -1 + x  |                                                                                                                                                                                                                                                                      |      /       2 |  |      /       2 |                                                                                                                                           |      /       2 |  |      /       2 |                                                                       
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        \x + \/  -1 + x  / *|x + \/  -1 + x  |                                                                                                                                           \x + \/  -1 + x  / *|x + \/  -1 + x  |
−x3(x2−1)32+3xx2−1+(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))ddxsign⁡(x+x2−1)(x+x2−1)∣x+x2−1∣+(4x2sin⁡2(atan2⁡(0,x2−1)2)δ(x2−1)−(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1)(xx2−1sign⁡(x2−1)(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)cos⁡(atan2⁡(0,x2−1)2)x2−1−1)+sin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(4x2δ(x2−1)+x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1+sign⁡(x2−1))cos⁡(atan2⁡(0,x2−1)2)x2−1sign⁡(x2−1))sign⁡(x+x2−1)(x+x2−1)∣x+x2−1∣−(xx2−1+1)(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))sign⁡(x+x2−1)(x+x2−1)2∣x+x2−1∣−(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))2sign⁡2(x+x2−1)(x+x2−1)2∣x+x2−1∣2- \frac{x^{3}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{3 x}{\sqrt{x^{2} - 1}} + \frac{\left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \frac{d}{d x} \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right) \left|{x + \sqrt{x^{2} - 1}}\right|} + \frac{\left(4 x^{2} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \delta\left(x^{2} - 1\right) - \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right) \left(\frac{x \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{x^{2} - 1} - 1\right) + \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \frac{\left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(4 x^{2} \delta\left(x^{2} - 1\right) + \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1} + \operatorname{sign}{\left(x^{2} - 1 \right)}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}}\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right) \left|{x + \sqrt{x^{2} - 1}}\right|} - \frac{\left(\frac{x}{\sqrt{x^{2} - 1}} + 1\right) \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \left|{x + \sqrt{x^{2} - 1}}\right|} - \frac{\left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right)^{2} \operatorname{sign}^{2}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \left|{x + \sqrt{x^{2} - 1}}\right|^{2}}
Simplificar
Tercera derivada [src] 
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                                                                                                                                                                                                                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  |        /       /      2\           /      2\\         /       /      2\           /      2\\                                                                                                                                                    /       /      2\           /      2\\                    |                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     /         /     /         2\\              \ |      2 |     2*\-1 + x /*DiracDelta\-1 + x /|       2 |     2*\-1 + x /*DiracDelta\-1 + x /|                                                                                                                                                  2 |     2*\-1 + x /*DiracDelta\-1 + x /|           /      2\|                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                       |                                                                                                                                                                                                                                                                                                                                                                                           /                                                                                                                                                                                                                                                                                                                          2                                                                                                                                             \                                _______________ |         |atan2\0, -1 + x /|     /      2\| |     x *|-1 + -------------------------------|    2*x *|-1 + -------------------------------|                                                                                                                                               4*x *|-1 + -------------------------------|*DiracDelta\-1 + x /|                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                       |                                                                                                           /             _______________                                                              \                                                                                                                                                                                    |                                                       /       /      2\           /      2\      2           /      2\       2           2/      2\ /      2\      2 /      2\           /      2   \\                   /       /      2\           /      2\\                    /       /      2\           /      2\\                       /       /      2\           /      2\\                       /       /      2\           /      2\\                    |                               /          2     |    x*cos|-----------------|*sign\-1 + x /| |        |                  /      2\         |         |                  /      2\         |     /      2\           /      2\      2           /      2\       2           2/      2\ /      2\      2 /      2\           /      2   \        |                  /      2\         |                    |    /     /         2\\|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         
                                                                                                                                                                                                                       |                                                                                                           |            /          2     /       /      2\           /      2\\    /     /         2\\| /                              /       /      2\           /      2\\                              \                                                                               |                                                       |     2*\-1 + x /*DiracDelta\-1 + x /   8*x *DiracDelta\-1 + x /   16*x *DiracDelta \-1 + x /*\-1 + x /   4*x *\-1 + x /*DiracDelta\-1 + x , 1/|     /      2\     |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\    2 |     2*\-1 + x /*DiracDelta\-1 + x /|      /      2\      2 |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\       2 |     2*\-1 + x /*DiracDelta\-1 + x /|           /      2\|                              /     -1 + x      |         \        2        /              | |        \              sign\-1 + x /         /         \              sign\-1 + x /         /   2*\-1 + x /*DiracDelta\-1 + x /   8*x *DiracDelta\-1 + x /   16*x *DiracDelta \-1 + x /*\-1 + x /   4*x *\-1 + x /*DiracDelta\-1 + x , 1/        \              sign\-1 + x /         /                    |    |atan2\0, -1 + x /||                            /                                                                                                                                                                                                                                                                                          /                              /       /      2\           /      2\\                              \                       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                                                                                                                                                                                                                                                          /                              /       /      2\           /      2\\                              \                       \                                                                                                                                                                                                                      /                                                                                                                                                                                                                                                                                          /                              /       /      2\           /      2\\                              \                       \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                       |                                                                                                           |           /     -1 + x      |     2*\-1 + x /*DiracDelta\-1 + x /|    |atan2\0, -1 + x /|| |                            2 |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\                |                            /          _______________                       \ |                                                       |-1 + ------------------------------- + ------------------------ - ------------------------------------ + -------------------------------------|*sign\-1 + x /   2*|-1 + -------------------------------|*sign\-1 + x /   x *|-1 + -------------------------------| *sign\-1 + x /   2*x *|-1 + -------------------------------|*sign\-1 + x /   12*x *|-1 + -------------------------------|*DiracDelta\-1 + x /|                             /   ------------- *|1 + --------------------------------------|*|-1 - ------------------------------------------ - ------------------------------------------- + ------------------------------- + ------------------------ - ------------------------------------ + ------------------------------------- + ---------------------------------------------------------------|*cos|-----------------||                            |                                                                                                                                                                                                                                                                                          |                            2 |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\                |                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                                                                                                                                                                                                                                                                                          |                            2 |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\                |                       |                                                                                                                                                                                                                      |                                                                                                                                                                                                                                                                                          |                            2 |     2*\-1 + x /*DiracDelta\-1 + x /|     /      2\                |                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                       |                                                                                                           |     x*   /   ------------- *|-1 + -------------------------------|*cos|-----------------|| |                           x *|-1 + -------------------------------|*sign\-1 + x /                |                            |         /          2        /     /         2\\| |                                                       |                  /      2\                     /      2\                        2/      2\                              /      2\            |                   |                  /      2\         |                    |                  /      2\         |                       |                  /      2\         |                       |                  /      2\         |                    |    /     /         2\\     /        /      2\  |                  _______________         | |                            2                                             2                                  /      2\                     /      2\                        2/      2\                              /      2\                                            /      2\                         |    \        2        /|                            |                                                                                     /             _______________                                                              \                                                      /          _______________                       \ |                           x *|-1 + -------------------------------|*sign\-1 + x /                |                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                                                                                     /             _______________                                                              \                                                      /          _______________                       \ |                           x *|-1 + -------------------------------|*sign\-1 + x /                |                       |                                                                                                                                                                                                                      |                                                                                     /             _______________                                                              \                                                      /          _______________                       \ |                           x *|-1 + -------------------------------|*sign\-1 + x /                |                       |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                       |                                                                                                           |         /        /      2\  |                  /      2\         |    \        2        /| |                              |                  /      2\         |                              |    /     /         2\\     |        /     -1 + x         |atan2\0, -1 + x /|| |             /      2\      2           /      2   \   \              sign\-1 + x /                 sign\-1 + x /                    sign \-1 + x /                          sign\-1 + x /            /                   \              sign\-1 + x /         /                    \              sign\-1 + x /         /                       \              sign\-1 + x /         /                       \              sign\-1 + x /         /                    |    |atan2\0, -1 + x /|   \/     sign\-1 + x /  |                 /          2             | \                      -1 + x                                        -1 + x                               sign\-1 + x /                 sign\-1 + x /                    sign \-1 + x /                          sign\-1 + x /                                        sign\-1 + x /                         /                       |                            |                                                                                     |            /          2     /       /      2\           /      2\\    /     /         2\\|                                                      |         /          2        /     /         2\\| |                              |                  /      2\         |                              |    /     /         2\\|                                                                                                                                                                           3                                                                                                                                                                        2                                                                                                                                                                                                                           |                                                                                     |            /          2     /       /      2\           /      2\\    /     /         2\\|                                                      |         /          2        /     /         2\\| |                              |                  /      2\         |                              |    /     /         2\\|                                                                                                                                                                                                                      |                                                                                     |            /          2     /       /      2\           /      2\\    /     /         2\\|                                                      |         /          2        /     /         2\\| |                              |                  /      2\         |                              |    /     /         2\\|                                                                                                                                                                                                                                                                                                                                                                  2                                                                                                                                                                                                                               
                                             //         /     /         2\\              \                                                                                             \                               |                                                                                                           |       \/     sign\-1 + x /  \              sign\-1 + x /         /                       | |   2           /      2\      \              sign\-1 + x /         /                     /      2\|    |atan2\0, -1 + x /|   x*|x +    /   ------------- *cos|-----------------||*|12*DiracDelta\-1 + x / + 8*x *DiracDelta\-1 + x , 1/ + -------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------ + -------------------------------------------------------- - --------------------------------------------------------- + ----------------------------------------------------------------|*cos|-----------------|                         |                /     -1 + x              |                                                                                                                                                                                                                                                                                                                                     |                            |                                        /         /     /         2\\              \ |           /     -1 + x      |     2*\-1 + x /*DiracDelta\-1 + x /|    |atan2\0, -1 + x /||                                                      |        /     -1 + x         |atan2\0, -1 + x /|| |   2           /      2\      \              sign\-1 + x /         /                     /      2\|    |atan2\0, -1 + x /||                                //         /     /         2\\              \                                                                                             \                              //         /     /         2\\              \                                                                                             \                                                                                //         /     /         2\\              \                                                                                             \ |                                        /         /     /         2\\              \ |           /     -1 + x      |     2*\-1 + x /*DiracDelta\-1 + x /|    |atan2\0, -1 + x /||                                                      |        /     -1 + x         |atan2\0, -1 + x /|| |   2           /      2\      \              sign\-1 + x /         /                     /      2\|    |atan2\0, -1 + x /||                        //         /     /         2\\              \                                                                                             \                                                   |                                        /         /     /         2\\              \ |           /     -1 + x      |     2*\-1 + x /*DiracDelta\-1 + x /|    |atan2\0, -1 + x /||                                                      |        /     -1 + x         |atan2\0, -1 + x /|| |   2           /      2\      \              sign\-1 + x /         /                     /      2\|    |atan2\0, -1 + x /||                                                //         /     /         2\\              \                                                                                             \                            //         /     /         2\\              \                                                                                             \                                                              //         /     /         2\\              \                                                                                             \                       
                                             ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                               |                                                                                                         2*|-1 + -------------------------------------------------------------------------------------|*|4*x *DiracDelta\-1 + x / + ------------------------------------------------------- + sign\-1 + x /|*cos|-----------------|     |      /        /      2\     \        2        /| |                                                                                                                                        2                                                                                                            2                                                           2                                                           2                                                            2                             |    \        2        /                         |               /   -------------          |                                                                                                                                                                                                                                                                                                                                     |                            |                                        |         |atan2\0, -1 + x /|     /      2\| |     x*   /   ------------- *|-1 + -------------------------------|*cos|-----------------||                                                      |x +    /   ------------- *cos|-----------------||*|4*x *DiracDelta\-1 + x / + ------------------------------------------------------- + sign\-1 + x /|*cos|-----------------||                                ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                              ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                                                                                ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          | |                                        |         |atan2\0, -1 + x /|     /      2\| |     x*   /   ------------- *|-1 + -------------------------------|*cos|-----------------||                                                      |x +    /   ------------- *cos|-----------------||*|4*x *DiracDelta\-1 + x / + ------------------------------------------------------- + sign\-1 + x /|*cos|-----------------||                        ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                                                   |                                        |         |atan2\0, -1 + x /|     /      2\| |     x*   /   ------------- *|-1 + -------------------------------|*cos|-----------------||                                                      |x +    /   ------------- *cos|-----------------||*|4*x *DiracDelta\-1 + x / + ------------------------------------------------------- + sign\-1 + x /|*cos|-----------------||                                                ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                            ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                                                              ||         |atan2\0, -1 + x /|     /      2\| /          _______________                       \                                          |                       
                                             ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |   2/    /       _________\\   |         /     /         2\\                                   /     /         2\\                         |                                                  2                                       | |                                                         2                                        |    \        2        /     \    \/     sign\-1 + x /                        / |                                                                                                                                  -1 + x                                                                                                       -1 + x                                                   /      2\                                                   /      2\                                                       -1 + x                              |                                                |              /        /      2\          |                                                                                                                                                                                                                                                                                                                                     |     /       _________\     |    /     /         2\\                 |    x*cos|-----------------|*sign\-1 + x /| |         /        /      2\  |                  /      2\         |    \        2        /|            /     /         2\\                       |      /        /      2\     \        2        /| |                                                         2                                        |    \        2        /|   /    /       _________\\     ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |       /       _________\     ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |    /    /       _________\\     /       _________\          /       _________\ ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              | |    /     /         2\\                 |    x*cos|-----------------|*sign\-1 + x /| |         /        /      2\  |                  /      2\         |    \        2        /|            /     /         2\\                       |      /        /      2\     \        2        /| |                                                         2                                        |    \        2        /|                        ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |   /    /       _________\\                        |    /     /         2\\                 |    x*cos|-----------------|*sign\-1 + x /| |         /        /      2\  |                  /      2\         |    \        2        /|            /     /         2\\                       |      /        /      2\     \        2        /| |                                                         2                                        |    \        2        /|     /       _________\                       2 ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |     /       _________\     ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |       /       _________\                      /         2  \ ||    x*cos|-----------------|*sign\-1 + x /| |         /          2        /     /         2\\|         /     /         2\\              |     /       _________\
                                             ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|  d |    |      /       2 ||   |   3    2|atan2\0, -1 + x /|           /      2   \           2|atan2\0, -1 + x /|           /      2\     \                                            -1 + x                                        / \                                                   -1 + x                                         /                                                                               \                                                                                                                                                                                                                                                                                                        \-1 + x /                                                   \-1 + x /                                                                                           /                                                \            \/     sign\-1 + x /          /                                                                                                                                                                                                                                                                                                                                     |     |      /       2 |     |   2|atan2\0, -1 + x /|     /      2\   |         \        2        /              | |       \/     sign\-1 + x /  \              sign\-1 + x /         /                       |      2    2|atan2\0, -1 + x /|           /      2\   \    \/     sign\-1 + x /                        / \                                                   -1 + x                                         /                       | d |    |      /       2 ||     ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|      3|      /       2 |     ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|  d |    |      /       2 ||     |      /       2 |         2|      /       2 | ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\| |   2|atan2\0, -1 + x /|     /      2\   |         \        2        /              | |       \/     sign\-1 + x /  \              sign\-1 + x /         /                       |      2    2|atan2\0, -1 + x /|           /      2\   \    \/     sign\-1 + x /                        / \                                                   -1 + x                                         /                       |     /         x      \ ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\| d |    |      /       2 ||     /         x      \ |   2|atan2\0, -1 + x /|     /      2\   |         \        2        /              | |       \/     sign\-1 + x /  \              sign\-1 + x /         /                       |      2    2|atan2\0, -1 + x /|           /      2\   \    \/     sign\-1 + x /                        / \                                                   -1 + x                                         /                       |     |      /       2 |     /         x      \  ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|     |      /       2 |     ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|      2|      /       2 | /         x      \   |        x   | ||         \        2        /              | |        /     -1 + x         |atan2\0, -1 + x /||        2|atan2\0, -1 + x /|     /      2\|     |      /       2 |
                                             ||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*---\sign\x + \/  -1 + x  //   |8*x *sin |-----------------|*DiracDelta\-1 + x , 1/ + 12*x*sin |-----------------|*DiracDelta\-1 + x / - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/  -1 + x  /   2*|sin |-----------------|*sign\-1 + x / - |1 + --------------------------------------|*|-1 + -------------------------------------------------------------------------------------| + 4*x *sin |-----------------|*DiracDelta\-1 + x / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*--\sign\x + \/  -1 + x  //   2*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /| *sign \x + \/  -1 + x  /   3*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /| *--\sign\x + \/  -1 + x  //*sign\x + \/  -1 + x  /   3*sign \x + \/  -1 + x  /*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*|sin |-----------------|*sign\-1 + x / - |1 + --------------------------------------|*|-1 + -------------------------------------------------------------------------------------| + 4*x *sin |-----------------|*DiracDelta\-1 + x / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|   2*|1 + ------------|*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*--\sign\x + \/  -1 + x  //   2*|1 + ------------|*|sin |-----------------|*sign\-1 + x / - |1 + --------------------------------------|*|-1 + -------------------------------------------------------------------------------------| + 4*x *sin |-----------------|*DiracDelta\-1 + x / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/  -1 + x  /   2*|1 + ------------| *||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*sign\x + \/  -1 + x  /   3*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /| *sign \x + \/  -1 + x  /*|1 + ------------|   |-1 + -------|*||1 + --------------------------------------|*|x +    /   ------------- *cos|-----------------|| + x*sin |-----------------|*sign\-1 + x /|*sign\x + \/  -1 + x  /
                                             ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |   2                           |         \        2        /                                   \        2        /                                                                                                                               _______________                                                                                                                                                                                                                                                                                                                                                                            _______________                                                                                                                                                                                                                                                                                                                                                                                                                                                                          2                                                                                                                                                                                                |                            |    \        2        /                 |                  _______________         | |                                                  2                                       |            \        2        /                                                                                                         _______________                                                                             | dx                             ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                              ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |  dx                                                                            ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              | |    \        2        /                 |                  _______________         | |                                                  2                                       |            \        2        /                                                                                                         _______________                                                                             |     |       _________| ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              | dx                             |       _________| |    \        2        /                 |                  _______________         | |                                                  2                                       |            \        2        /                                                                                                         _______________                                                                             |                            |       _________|  ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                            ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                          |       _________|   |           2| ||                  _______________         | |      /        /      2\     \        2        /|         \        2        /              |                       
                                             ||                 /          2             | \    \/     sign\-1 + x /                        /                                          | dx                            |                                                                                                                                                                                                                /          2                                                                                                                                                                                                                                                                                                                                                                               /          2                                                                                                                                                                                                                                                                                                                                                                                                                                                                        -1 + x                                                                                                                                                                                                 |                            |                                        |                 /          2             | \                                            -1 + x                                        /                                                                                                                                       /          2                                                                                 |                                ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                              ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                                                                                ||                 /          2             | \    \/     sign\-1 + x /                        /                                          | |                                        |                 /          2             | \                                            -1 + x                                        /                                                                                                                                       /          2                                                                                 |     |      /       2 | ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                                |      /       2 | |                                        |                 /          2             | \                                            -1 + x                                        /                                                                                                                                       /          2                                                                                 |                            |      /       2 |  ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                            ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                          |      /       2 |   \     -1 + x / ||                 /          2             | \    \/     sign\-1 + x /                        /                                          |                       
                                             ||                /     -1 + x              |                                                                                             |                               |                                                                                                                                                                                                               /     -1 + x                                                                                                                                                                                                                                                                                                                                                                               /     -1 + x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                |                            |                                        |                /     -1 + x              |                                                                                                                                                                                                                                   /     -1 + x                                                                                  |                                ||                /     -1 + x              |                                                                                             |                              ||                /     -1 + x              |                                                                                             |                                                                                ||                /     -1 + x              |                                                                                             | |                                        |                /     -1 + x              |                                                                                                                                                                                                                                   /     -1 + x                                                                                  |     \    \/  -1 + x  / ||                /     -1 + x              |                                                                                             |                                \    \/  -1 + x  / |                                        |                /     -1 + x              |                                                                                                                                                                                                                                   /     -1 + x                                                                                  |                            \    \/  -1 + x  /  ||                /     -1 + x              |                                                                                             |                            ||                /     -1 + x              |                                                                                             |                          \    \/  -1 + x  /                  ||                /     -1 + x              |                                                                                             |                       
                                             ||               /   -------------          |                                                                                             |                               |                                                                                                                                                                                                              /   -------------                                                                                                                                                                                                                                                                                                                                                                          /   -------------                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |                            |                                        |               /   -------------          |                                                                                                                                                                                                                                  /   -------------                                                                              |                                ||               /   -------------          |                                                                                             |                              ||               /   -------------          |                                                                                             |                                                                                ||               /   -------------          |                                                                                             | |                                        |               /   -------------          |                                                                                                                                                                                                                                  /   -------------                                                                              |                        ||               /   -------------          |                                                                                             |                                                   |                                        |               /   -------------          |                                                                                                                                                                                                                                  /   -------------                                                                              |                                                ||               /   -------------          |                                                                                             |                            ||               /   -------------          |                                                                                             |                                                              ||               /   -------------          |                                                                                             |                       
                      2              4       ||              /        /      2\          |                                                                                             |                               |                                                                                                                                                                                                             /        /      2\                                                                                                                                                                                                                                                                                                                                                                         /        /      2\                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            |                            |                                        |              /        /      2\          |                                                                                                                                                                                                                                 /        /      2\                                                                              |                                ||              /        /      2\          |                                                                                             |                              ||              /        /      2\          |                                                                                             |                                                                                ||              /        /      2\          |                                                                                             | |                                        |              /        /      2\          |                                                                                                                                                                                                                                 /        /      2\                                                                              |                        ||              /        /      2\          |                                                                                             |                                                   |                                        |              /        /      2\          |                                                                                                                                                                                                                                 /        /      2\                                                                              |                                                ||              /        /      2\          |                                                                                             |                            ||              /        /      2\          |                                                                                             |                                                              ||              /        /      2\          |                                                                                             |                       
     3             6*x            3*x        \\            \/     sign\-1 + x /          /                                                                                             /                               \                                                                                                                                                                                                           \/     sign\-1 + x /                                                                                                                                                                                                                                                                                                                                                                       \/     sign\-1 + x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            /                            \                                        \            \/     sign\-1 + x /          /                                                                                                                                                                                                                               \/     sign\-1 + x /                                                                              /                                \\            \/     sign\-1 + x /          /                                                                                             /                              \\            \/     sign\-1 + x /          /                                                                                             /                                                                                \\            \/     sign\-1 + x /          /                                                                                             / \                                        \            \/     sign\-1 + x /          /                                                                                                                                                                                                                               \/     sign\-1 + x /                                                                              /                        \\            \/     sign\-1 + x /          /                                                                                             /                                                   \                                        \            \/     sign\-1 + x /          /                                                                                                                                                                                                                               \/     sign\-1 + x /                                                                              /                                                \\            \/     sign\-1 + x /          /                                                                                             /                            \\            \/     sign\-1 + x /          /                                                                                             /                                                              \\            \/     sign\-1 + x /          /                                                                                             /                       
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\/  -1 + x     \-1 + x /      \-1 + x /                                                                       \x + \/  -1 + x  /*|x + \/  -1 + x  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \x + \/  -1 + x  /*|x + \/  -1 + x  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       \x + \/  -1 + x  /*|x + \/  -1 + x  |                                                                                                                                                                                                                                                                          |      /       2 |  |      /       2 |                                                                                                                                                |      /       2 |  |      /       2 |                                                                                                                                                                                                                                                                                                                                                            |      /       2 |  |      /       2 |                                                                                                                                                                                                                                                                                                                                                          |      /       2 |  |      /       2 |                                                                                                                                                                                                                                                                                            |      /       2 |  |      /       2 |                                                                                                                                                                                                                                                                                          |      /       2 |  |      /       2 |                                                                                                                                                     |      /       2 |  |      /       2 |                                                                                                                                              /       2  |      /       2 |  |      /       2 |                                                               
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3x4(x2−1)52−6x2(x2−1)32+3x2−1+(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))d2dx2sign⁡(x+x2−1)(x+x2−1)∣x+x2−1∣+2(4x2sin⁡2(atan2⁡(0,x2−1)2)δ(x2−1)−(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1)(xx2−1sign⁡(x2−1)(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)cos⁡(atan2⁡(0,x2−1)2)x2−1−1)+sin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(4x2δ(x2−1)+x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1+sign⁡(x2−1))cos⁡(atan2⁡(0,x2−1)2)x2−1sign⁡(x2−1))ddxsign⁡(x+x2−1)(x+x2−1)∣x+x2−1∣+(8x3sin⁡2(atan2⁡(0,x2−1)2)δ(1)(x2−1)+12xsin⁡2(atan2⁡(0,x2−1)2)δ(x2−1)+x(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(8x2δ(1)(x2−1)+12x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)δ(x2−1)x2−1+x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)2sign⁡(x2−1)(x2−1)2−2x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)(x2−1)2+12δ(x2−1)+2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1+(−16x2(x2−1)(δ(x2−1))2sign⁡2(x2−1)+4x2(x2−1)δ(1)(x2−1)sign⁡(x2−1)+8x2δ(x2−1)sign⁡(x2−1)+2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1)cos⁡(atan2⁡(0,x2−1)2)x2−1sign⁡(x2−1)−x2−1sign⁡(x2−1)(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1)(−16x2(x2−1)(δ(x2−1))2sign⁡2(x2−1)+4x2(x2−1)δ(1)(x2−1)sign⁡(x2−1)+4x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)δ(x2−1)sign⁡(x2−1)+8x2δ(x2−1)sign⁡(x2−1)−x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)2x2−1−2x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)x2−1+2(x2−1)δ(x2−1)sign⁡(x2−1)−1)cos⁡(atan2⁡(0,x2−1)2)x2−1−2(xx2−1sign⁡(x2−1)(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)cos⁡(atan2⁡(0,x2−1)2)x2−1−1)(4x2δ(x2−1)+x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1+sign⁡(x2−1))cos⁡(atan2⁡(0,x2−1)2)x2−1sign⁡(x2−1))sign⁡(x+x2−1)(x+x2−1)∣x+x2−1∣−2(xx2−1+1)(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))ddxsign⁡(x+x2−1)(x+x2−1)2∣x+x2−1∣−2(xx2−1+1)(4x2sin⁡2(atan2⁡(0,x2−1)2)δ(x2−1)−(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1)(xx2−1sign⁡(x2−1)(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)cos⁡(atan2⁡(0,x2−1)2)x2−1−1)+sin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(4x2δ(x2−1)+x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1+sign⁡(x2−1))cos⁡(atan2⁡(0,x2−1)2)x2−1sign⁡(x2−1))sign⁡(x+x2−1)(x+x2−1)2∣x+x2−1∣−3(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))2sign⁡(x+x2−1)ddxsign⁡(x+x2−1)(x+x2−1)2∣x+x2−1∣2−3(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))(4x2sin⁡2(atan2⁡(0,x2−1)2)δ(x2−1)−(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1)(xx2−1sign⁡(x2−1)(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)cos⁡(atan2⁡(0,x2−1)2)x2−1−1)+sin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(4x2δ(x2−1)+x2(2(x2−1)δ(x2−1)sign⁡(x2−1)−1)sign⁡(x2−1)x2−1+sign⁡(x2−1))cos⁡(atan2⁡(0,x2−1)2)x2−1sign⁡(x2−1))sign⁡2(x+x2−1)(x+x2−1)2∣x+x2−1∣2+(x2x2−1−1)(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))sign⁡(x+x2−1)(x+x2−1)2x2−1∣x+x2−1∣+2(xx2−1+1)2(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))sign⁡(x+x2−1)(x+x2−1)3∣x+x2−1∣+3(xx2−1+1)(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))2sign⁡2(x+x2−1)(x+x2−1)3∣x+x2−1∣2+2(xsin⁡2(atan2⁡(0,x2−1)2)sign⁡(x2−1)+(x+x2−1sign⁡(x2−1)cos⁡(atan2⁡(0,x2−1)2))(xcos⁡(atan2⁡(0,x2−1)2)sign⁡(x2−1)x2−1sign⁡(x2−1)+1))3sign⁡3(x+x2−1)(x+x2−1)3∣x+x2−1∣3\frac{3 x^{4}}{\left(x^{2} - 1\right)^{\frac{5}{2}}} - \frac{6 x^{2}}{\left(x^{2} - 1\right)^{\frac{3}{2}}} + \frac{3}{\sqrt{x^{2} - 1}} + \frac{\left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \frac{d^{2}}{d x^{2}} \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right) \left|{x + \sqrt{x^{2} - 1}}\right|} + \frac{2 \left(4 x^{2} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \delta\left(x^{2} - 1\right) - \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right) \left(\frac{x \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{x^{2} - 1} - 1\right) + \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \frac{\left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(4 x^{2} \delta\left(x^{2} - 1\right) + \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1} + \operatorname{sign}{\left(x^{2} - 1 \right)}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}}\right) \frac{d}{d x} \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right) \left|{x + \sqrt{x^{2} - 1}}\right|} + \frac{\left(8 x^{3} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \delta^{\left( 1 \right)}\left( x^{2} - 1 \right) + 12 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \delta\left(x^{2} - 1\right) + \frac{x \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(8 x^{2} \delta^{\left( 1 \right)}\left( x^{2} - 1 \right) + \frac{12 x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \delta\left(x^{2} - 1\right)}{x^{2} - 1} + \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right)^{2} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\left(x^{2} - 1\right)^{2}} - \frac{2 x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{\left(x^{2} - 1\right)^{2}} + 12 \delta\left(x^{2} - 1\right) + \frac{2 \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1} + \frac{\left(- \frac{16 x^{2} \left(x^{2} - 1\right) \left(\delta\left(x^{2} - 1\right)\right)^{2}}{\operatorname{sign}^{2}{\left(x^{2} - 1 \right)}} + \frac{4 x^{2} \left(x^{2} - 1\right) \delta^{\left( 1 \right)}\left( x^{2} - 1 \right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} + \frac{8 x^{2} \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} + \frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} - \frac{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right) \left(- \frac{16 x^{2} \left(x^{2} - 1\right) \left(\delta\left(x^{2} - 1\right)\right)^{2}}{\operatorname{sign}^{2}{\left(x^{2} - 1 \right)}} + \frac{4 x^{2} \left(x^{2} - 1\right) \delta^{\left( 1 \right)}\left( x^{2} - 1 \right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} + \frac{4 x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} + \frac{8 x^{2} \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right)^{2}}{x^{2} - 1} - \frac{2 x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right)}{x^{2} - 1} + \frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{x^{2} - 1} - \frac{2 \left(\frac{x \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{x^{2} - 1} - 1\right) \left(4 x^{2} \delta\left(x^{2} - 1\right) + \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1} + \operatorname{sign}{\left(x^{2} - 1 \right)}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}}\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right) \left|{x + \sqrt{x^{2} - 1}}\right|} - \frac{2 \left(\frac{x}{\sqrt{x^{2} - 1}} + 1\right) \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \frac{d}{d x} \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \left|{x + \sqrt{x^{2} - 1}}\right|} - \frac{2 \left(\frac{x}{\sqrt{x^{2} - 1}} + 1\right) \left(4 x^{2} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \delta\left(x^{2} - 1\right) - \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right) \left(\frac{x \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{x^{2} - 1} - 1\right) + \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \frac{\left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(4 x^{2} \delta\left(x^{2} - 1\right) + \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1} + \operatorname{sign}{\left(x^{2} - 1 \right)}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}}\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \left|{x + \sqrt{x^{2} - 1}}\right|} - \frac{3 \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right)^{2} \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)} \frac{d}{d x} \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \left|{x + \sqrt{x^{2} - 1}}\right|^{2}} - \frac{3 \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \left(4 x^{2} \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \delta\left(x^{2} - 1\right) - \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right) \left(\frac{x \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{x^{2} - 1} - 1\right) + \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \frac{\left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(4 x^{2} \delta\left(x^{2} - 1\right) + \frac{x^{2} \left(\frac{2 \left(x^{2} - 1\right) \delta\left(x^{2} - 1\right)}{\operatorname{sign}{\left(x^{2} - 1 \right)}} - 1\right) \operatorname{sign}{\left(x^{2} - 1 \right)}}{x^{2} - 1} + \operatorname{sign}{\left(x^{2} - 1 \right)}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}}\right) \operatorname{sign}^{2}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \left|{x + \sqrt{x^{2} - 1}}\right|^{2}} + \frac{\left(\frac{x^{2}}{x^{2} - 1} - 1\right) \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{2} \sqrt{x^{2} - 1} \left|{x + \sqrt{x^{2} - 1}}\right|} + \frac{2 \left(\frac{x}{\sqrt{x^{2} - 1}} + 1\right)^{2} \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right) \operatorname{sign}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{3} \left|{x + \sqrt{x^{2} - 1}}\right|} + \frac{3 \left(\frac{x}{\sqrt{x^{2} - 1}} + 1\right) \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right)^{2} \operatorname{sign}^{2}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{3} \left|{x + \sqrt{x^{2} - 1}}\right|^{2}} + \frac{2 \left(x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)} + \left(x + \sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)}\right) \left(\frac{x \cos{\left(\frac{\operatorname{atan_{2}}{\left(0,x^{2} - 1 \right)}}{2} \right)} \operatorname{sign}{\left(x^{2} - 1 \right)}}{\sqrt{\frac{x^{2} - 1}{\operatorname{sign}{\left(x^{2} - 1 \right)}}}} + 1\right)\right)^{3} \operatorname{sign}^{3}{\left(x + \sqrt{x^{2} - 1} \right)}}{\left(x + \sqrt{x^{2} - 1}\right)^{3} \left|{x + \sqrt{x^{2} - 1}}\right|^{3}}
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Gráfico
Derivada de xsqrt(x^2-1)+ln|x+sqrt(x^2-1)|
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