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Derivada de la función/ x^2+3/ xln|x+√x^2+3|-√x^2+3

Derivada de xln|x+√x^2+3|-√x^2+3

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
     /|         2    |\        2    
     ||      ___     ||     ___     
x*log\|x + \/ x   + 3|/ - \/ x   + 3
(−(x)2+xlog⁡(∣((x)2+x)+3∣))+3\left(- \left(\sqrt{x}\right)^{2} + x \log{\left(\left|{\left(\left(\sqrt{x}\right)^{2} + x\right) + 3}\right| \right)}\right) + 3 
x*log(Abs(x + (sqrt(x))^2 + 3)) - (sqrt(x))^2 + 3
Primera derivada [src] 
       /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                                      
       |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                                      
       |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                                      
     x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)      /|         2    |\
       \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                    ||      ___     ||
-1 + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + log\|x + \/ x   + 3|/
                                                                                        |         2    |                                                                                                
                                                                                        |      ___     |                                                                                                
                                                                              (3 + 2*x)*|x + \/ x   + 3|
x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))sign⁡(2x+3)(2x+3)∣((x)2+x)+3∣+log⁡(∣((x)2+x)+3∣)−1\frac{x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{\left(\left(\sqrt{x}\right)^{2} + x\right) + 3}\right|} + \log{\left(\left|{\left(\left(\sqrt{x}\right)^{2} + x\right) + 3}\right| \right)} - 1
Simplificar
Segunda derivada [src] 
                                                                                                                                                                                /                                                            /       2/atan2(0, x)\      2/atan2(0, x)\          2/atan2(0, x)\                        2/atan2(0, x)\              \                                                                                     /             2/atan2(0, x)\        2/atan2(0, x)\\              \                                                                                                                                                                              2                                                                                                                                                                                                                                                                                                                                                                                     
  /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                   |                                                            |    cos |-----------|   sin |-----------|   2*x*cos |-----------|*DiracDelta(x)   2*x*sin |-----------|*DiracDelta(x)|                                                                                     |        x*cos |-----------|   x*sin |-----------||              |                   /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                       /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                           /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \              
  |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                   |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |        \     2     /       \     2     /           \     2     /                         \     2     /              |        2/atan2(0, x)\    2/atan2(0, x)\     /   2/atan2(0, x)\      2/atan2(0, x)\\ |              \     2     /         \     2     /|              |                   |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                       |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                           |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |              
  |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                 x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*sign(3 + 2*x)     |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|      2                |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                           |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|              
2*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)     |\        \     2     /               \     2     /        / |         sign(x)             sign(x)                          2                                     2                |         \     2     /     \     2     /     \    \     2     /       \     2     // \              sign(x)               sign(x)      /              |                 x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x)   4*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x)   2*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)
  \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                   \                                                            \                                                          sign (x)                              sign (x)             /                                                                                                                                                      /                   \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                       \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                           \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //              
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                 |3 + 2*x|                                                                                                                                                                                                                                                             |3 + 2*x|                                                                                                                                                                                                                                                                       3                                                                                                                                                                         |3 + 2*x|                                                                                                                                                                     (3 + 2*x)*|3 + 2*x|                                                                             
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              (3 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                        
-----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            3 + 2*x
4x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))δ(2x+3)∣2x+3∣+x(−2(sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3)δ(x)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(2xsin⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−2xcos⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)+4sin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2))sign⁡(2x+3)∣2x+3∣−2x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))sign⁡(2x+3)(2x+3)∣2x+3∣−x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))2sign⁡2(2x+3)(2x+3)3+2(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))sign⁡(2x+3)∣2x+3∣2x+3\frac{\frac{4 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta\left(2 x + 3\right)}{\left|{2 x + 3}\right|} + \frac{x \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|} - \frac{2 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{2 x + 3}\right|} - \frac{x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}} + \frac{2 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|}}{2 x + 3}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       /                                                            /                                                                                                                                                                      2       2/atan2(0, x)\                 2       2/atan2(0, x)\\                                                                                                                                                                                                                                                                                                 \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                       |                                                            |                                                                                                                                                        4*x*DiracDelta (x)*cos |-----------|   4*x*DiracDelta (x)*sin |-----------||                                                                                                                                                                                                                                                                                                 |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     
                                                                                                                                                               2                    /                                                            /       2/atan2(0, x)\      2/atan2(0, x)\          2/atan2(0, x)\                        2/atan2(0, x)\              \                                                                                     /             2/atan2(0, x)\        2/atan2(0, x)\\              \                                                                                                                                                                                                                                                                                                                                                                                        |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |       2/atan2(0, x)\                      2/atan2(0, x)\                      2/atan2(0, x)\                         2/atan2(0, x)\                                           \     2     /                          \     2     /|                                           /             2/atan2(0, x)\        2/atan2(0, x)\\                                                              /       2/atan2(0, x)\      2/atan2(0, x)\          2/atan2(0, x)\                        2/atan2(0, x)\              \              |                                                                                                                                                                                2                                                                                                                                                                                                               /                                                            /       2/atan2(0, x)\      2/atan2(0, x)\          2/atan2(0, x)\                        2/atan2(0, x)\              \                                                                                     /             2/atan2(0, x)\        2/atan2(0, x)\\              \                                                                                                                                                                                                                                                                                                                                                                              2                                         /                                                            /       2/atan2(0, x)\      2/atan2(0, x)\          2/atan2(0, x)\                        2/atan2(0, x)\              \                                                                                     /             2/atan2(0, x)\        2/atan2(0, x)\\              \                                    /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \ /                                                            /       2/atan2(0, x)\      2/atan2(0, x)\          2/atan2(0, x)\                        2/atan2(0, x)\              \                                                                                     /             2/atan2(0, x)\        2/atan2(0, x)\\              \                                                                                                                                                                  3                                                                                                                                                                                                         
    /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                     |                                                            |    cos |-----------|   sin |-----------|   2*x*cos |-----------|*DiracDelta(x)   2*x*sin |-----------|*DiracDelta(x)|                                                                                     |        x*cos |-----------|   x*sin |-----------||              |                    /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                         /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                     ||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|- 2*sin |-----------|*DiracDelta(x) + 2*cos |-----------|*DiracDelta(x) + x*cos |-----------|*DiracDelta(x, 1) - x*sin |-----------|*DiracDelta(x, 1) - ------------------------------------ + ------------------------------------|                                           |        x*cos |-----------|   x*sin |-----------||                                                              |    cos |-----------|   sin |-----------|   2*x*cos |-----------|*DiracDelta(x)   2*x*sin |-----------|*DiracDelta(x)|              |                     /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                       /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                              |                                                            |    cos |-----------|   sin |-----------|   2*x*cos |-----------|*DiracDelta(x)   2*x*sin |-----------|*DiracDelta(x)|                                                                                     |        x*cos |-----------|   x*sin |-----------||              |                            /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                            /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                                          |                                                            |    cos |-----------|   sin |-----------|   2*x*cos |-----------|*DiracDelta(x)   2*x*sin |-----------|*DiracDelta(x)|                                                                                     |        x*cos |-----------|   x*sin |-----------||              |                                    |                                                            |        x*cos |-----------|   x*sin |-----------||                                          | |                                                            |    cos |-----------|   sin |-----------|   2*x*cos |-----------|*DiracDelta(x)   2*x*sin |-----------|*DiracDelta(x)|                                                                                     |        x*cos |-----------|   x*sin |-----------||              |       /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \                                 /                                                            /             2/atan2(0, x)\        2/atan2(0, x)\\                                          \              
    |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                     |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |        \     2     /       \     2     /           \     2     /                         \     2     /              |        2/atan2(0, x)\    2/atan2(0, x)\     /   2/atan2(0, x)\      2/atan2(0, x)\\ |              \     2     /         \     2     /|              |                    |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                         |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                     |\        \     2     /               \     2     /        / \        \     2     /                       \     2     /                       \     2     /                          \     2     /                                  sign(x)                                sign(x)               /   /   2/atan2(0, x)\      2/atan2(0, x)\\ |              \     2     /         \     2     /|                      /   2/atan2(0, x)\      2/atan2(0, x)\\ |        \     2     /       \     2     /           \     2     /                         \     2     /              |              |                     |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                       |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                              |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |        \     2     /       \     2     /           \     2     /                         \     2     /              |        2/atan2(0, x)\    2/atan2(0, x)\     /   2/atan2(0, x)\      2/atan2(0, x)\\ |              \     2     /         \     2     /|              |                            |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                            |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                                          |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |        \     2     /       \     2     /           \     2     /                         \     2     /              |        2/atan2(0, x)\    2/atan2(0, x)\     /   2/atan2(0, x)\      2/atan2(0, x)\\ |              \     2     /         \     2     /|              |                         2          |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\| |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |        \     2     /       \     2     /           \     2     /                         \     2     /              |        2/atan2(0, x)\    2/atan2(0, x)\     /   2/atan2(0, x)\      2/atan2(0, x)\\ |              \     2     /         \     2     /|              |       |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |                                 |                                                            |        x*cos |-----------|   x*sin |-----------||                                          |              
    |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|      2            3*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*sign(3 + 2*x)      |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                         |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                 2*x*|------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + |sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x, 1) + 2*|sin |-----------| - cos |-----------||*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------|*DiracDelta(x)|*sign(3 + 2*x)       |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|      2                |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                          8*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*DiracDelta(3 + 2*x)        |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                            |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|                                      4*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|*sign(3 + 2*x)   3*x*sign (3 + 2*x)*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|1 + ----------------- - ----------------- - ----------------------------------- + -----------------------------------| + 4*cos |-----------|*sin |-----------| - 2*|sin |-----------| - cos |-----------||*|3 + x + ------------------- - -------------------|*DiracDelta(x)|       |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|      3                          |/       2/atan2(0, x)\              2/atan2(0, x)\        \ |              \     2     /         \     2     /|          2/atan2(0, x)\    2/atan2(0, x)\|              
  3*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x)     |\        \     2     /               \     2     /        / |         sign(x)             sign(x)                          2                                     2                |         \     2     /     \     2     /     \    \     2     /       \     2     // \              sign(x)               sign(x)      /              |                 12*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x)   6*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)       |                                                                                                                                                 2                                                                                                                                                  \    \     2     /       \     2     // \              sign(x)               sign(x)      /                      \    \     2     /       \     2     // |         sign(x)             sign(x)                          2                                     2                |              |                 6*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x)   8*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x, 1)       |\        \     2     /               \     2     /        / |         sign(x)             sign(x)                          2                                     2                |         \     2     /     \     2     /     \    \     2     /       \     2     // \              sign(x)               sign(x)      /              |                       16*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*DiracDelta(3 + 2*x)   12*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *DiracDelta(3 + 2*x)*sign(3 + 2*x)       |\        \     2     /               \     2     /        / |         sign(x)             sign(x)                          2                                     2                |         \     2     /     \     2     /     \    \     2     /       \     2     // \              sign(x)               sign(x)      /              |                                    \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     // |\        \     2     /               \     2     /        / |         sign(x)             sign(x)                          2                                     2                |         \     2     /     \     2     /     \    \     2     /       \     2     // \              sign(x)               sign(x)      /              |   2*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------|| *sign (3 + 2*x)*|3 + 2*x|   8*x*||1 + cos |-----------|*sign(x) - sin |-----------|*sign(x)|*|3 + x + ------------------- - -------------------| + 4*x*cos |-----------|*sin |-----------||*sign(3 + 2*x)
    \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                     \                                                            \                                                          sign (x)                              sign (x)             /                                                                                                                                                      /                    \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                         \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                     \                                                                                                                                             sign (x)                                                                                                                                                                                                                                                                                                        \                                                          sign (x)                              sign (x)             /              /                     \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                       \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                              \                                                            \                                                          sign (x)                              sign (x)             /                                                                                                                                                      /                            \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                            \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                                          \                                                            \                                                          sign (x)                              sign (x)             /                                                                                                                                                      /                                                                                                                                                                                                \                                                            \                                                          sign (x)                              sign (x)             /                                                                                                                                                      /       \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //                                 \\        \     2     /               \     2     /        / \              sign(x)               sign(x)      /           \     2     /     \     2     //              
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                                                                                             3                                                                                                                                                                                                                                                             |3 + 2*x|                                                                                                                                                                                                                                                                |3 + 2*x|                                                                                                                                                                    (3 + 2*x)*|3 + 2*x|                                                                                                                                                                                                                                                                                                                                                                                     |3 + 2*x|                                                                                                                                                                                                                                                                                                                                                                                                      4                                                                                                                                                                           |3 + 2*x|                                                                                                                                                                                                                                                                       |3 + 2*x|                                                                                                                                                                                                                                                                (3 + 2*x)*|3 + 2*x|                                                                                                                                                                                          3                                                                                                                                                                                                                                                                    (3 + 2*x)*|3 + 2*x|                                                                                                                                                                                                                                                                                                                                                                                                                                         3                                                                                                                                                                                                                                                                                                                                                            6                                                                                                                                                                                2                                                                                      
                                                                                    (3 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  (3 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                         (3 + 2*x)                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        (3 + 2*x)                                                                                                                                                                                                                                                                                                                                                    (3 + 2*x)                                                                                                                                                                        (3 + 2*x) *|3 + 2*x|                                                                            
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8x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))δ(1)(2x+3)∣2x+3∣+8x(−2(sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3)δ(x)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(2xsin⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−2xcos⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)+4sin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2))δ(2x+3)∣2x+3∣−2x((sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3)δ(1)(x)+2(sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(2xsin⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−2xcos⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)δ(x)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(4xsin⁡2(atan2⁡(0,x)2)(δ(x))2sign⁡(x)−xsin⁡2(atan2⁡(0,x)2)δ(1)(x)−4xcos⁡2(atan2⁡(0,x)2)(δ(x))2sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)δ(1)(x)−2sin⁡2(atan2⁡(0,x)2)δ(x)+2cos⁡2(atan2⁡(0,x)2)δ(x))sign⁡2(x))sign⁡(2x+3)∣2x+3∣−16x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))δ(2x+3)(2x+3)∣2x+3∣−4x(−2(sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3)δ(x)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(2xsin⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−2xcos⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)+4sin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2))sign⁡(2x+3)(2x+3)∣2x+3∣+8x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))sign⁡(2x+3)(2x+3)2∣2x+3∣−12x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))2δ(2x+3)sign⁡(2x+3)(2x+3)3−3x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))(−2(sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3)δ(x)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(2xsin⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−2xcos⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)+4sin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2))sign⁡2(2x+3)(2x+3)3+6x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))2sign⁡2(2x+3)(2x+3)4+2x(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))3∣2x+3∣sign⁡3(2x+3)(2x+3)6+12(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))δ(2x+3)∣2x+3∣+3(−2(sin⁡2(atan2⁡(0,x)2)−cos⁡2(atan2⁡(0,x)2))(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3)δ(x)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(2xsin⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−2xcos⁡2(atan2⁡(0,x)2)δ(x)sign⁡2(x)−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)+4sin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2))sign⁡(2x+3)∣2x+3∣−6(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))sign⁡(2x+3)(2x+3)∣2x+3∣−3(4xsin⁡2(atan2⁡(0,x)2)cos⁡2(atan2⁡(0,x)2)+(−sin⁡2(atan2⁡(0,x)2)sign⁡(x)+cos⁡2(atan2⁡(0,x)2)sign⁡(x)+1)(−xsin⁡2(atan2⁡(0,x)2)sign⁡(x)+xcos⁡2(atan2⁡(0,x)2)sign⁡(x)+x+3))2sign⁡2(2x+3)(2x+3)32x+3\frac{\frac{8 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta^{\left( 1 \right)}\left( 2 x + 3 \right)}{\left|{2 x + 3}\right|} + \frac{8 x \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \delta\left(2 x + 3\right)}{\left|{2 x + 3}\right|} - \frac{2 x \left(\left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta^{\left( 1 \right)}\left( x \right) + 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) \delta\left(x\right) + \frac{\left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \left(\delta\left(x\right)\right)^{2}}{\operatorname{sign}{\left(x \right)}} - x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta^{\left( 1 \right)}\left( x \right) - \frac{4 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \left(\delta\left(x\right)\right)^{2}}{\operatorname{sign}{\left(x \right)}} + x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta^{\left( 1 \right)}\left( x \right) - 2 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right) + 2 \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)\right)}{\operatorname{sign}^{2}{\left(x \right)}}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|} - \frac{16 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta\left(2 x + 3\right)}{\left(2 x + 3\right) \left|{2 x + 3}\right|} - \frac{4 x \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{2 x + 3}\right|} + \frac{8 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{2} \left|{2 x + 3}\right|} - \frac{12 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \delta\left(2 x + 3\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}} - \frac{3 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}} + \frac{6 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{4}} + \frac{2 x \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{3} \left|{2 x + 3}\right| \operatorname{sign}^{3}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{6}} + \frac{12 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \delta\left(2 x + 3\right)}{\left|{2 x + 3}\right|} + \frac{3 \left(- 2 \left(\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} - \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right) \delta\left(x\right) + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(\frac{2 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{2 x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \delta\left(x\right)}{\operatorname{sign}^{2}{\left(x \right)}} - \frac{\sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{\cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + 1\right) + 4 \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left|{2 x + 3}\right|} - \frac{6 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right) \operatorname{sign}{\left(2 x + 3 \right)}}{\left(2 x + 3\right) \left|{2 x + 3}\right|} - \frac{3 \left(4 x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} + \left(- \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)} \operatorname{sign}{\left(x \right)} + 1\right) \left(- \frac{x \sin^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + \frac{x \cos^{2}{\left(\frac{\operatorname{atan_{2}}{\left(0,x \right)}}{2} \right)}}{\operatorname{sign}{\left(x \right)}} + x + 3\right)\right)^{2} \operatorname{sign}^{2}{\left(2 x + 3 \right)}}{\left(2 x + 3\right)^{3}}}{2 x + 3}
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    © Sr Examen – Калькулятор