Sr Examen

Otras calculadoras

Derivada de la función/ sqrt(x)/ x^2-a^2/ y=ln|x+sqrt(x)/(x^2-a^2)|

Derivada de y=ln|x+sqrt(x)/(x^2-a^2)|

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   /|       ___ |\
   ||     \/ x  ||
log||x + -------||
   ||     2    2||
   \|    x  - a |/
log⁡(∣x−a2+x2+x∣)\log{\left(\left|{\frac{\sqrt{x}}{- a^{2} + x^{2}} + x}\right| \right)} 
log(Abs(x + sqrt(x)/(x^2 - a^2)))
Primera derivada [src] 
/                  /      /       1       \                   \   /  /       1       \                   \            \                  
|                  |    re|---------------|                   |   |im|---------------|                   |            |                  
|/      /   ___ \\ |      |  ___ / 2    2\|       /    3/2   \|   |  |  ___ / 2    2\|       /    3/2   \|   /   ___ \|     /       ___ \
||      | \/ x  || |      \\/ x *\x  - a //       |   x      ||   |  \\/ x *\x  - a //       |   x      ||   | \/ x  ||     |     \/ x  |
||x + re|-------||*|1 + ------------------- - 2*re|----------|| + |------------------- - 2*im|----------||*im|-------||*sign|x + -------|
||      | 2    2|| |             2                |         2||   |         2                |         2||   | 2    2||     |     2    2|
|\      \x  - a // |                              |/ 2    2\ ||   |                          |/ 2    2\ ||   \x  - a /|     \    x  - a /
\                  \                              \\x  - a / //   \                          \\x  - a / //            /                  
-----------------------------------------------------------------------------------------------------------------------------------------
                                                       /       ___ \ |       ___ |                                                       
                                                       |     \/ x  | |     \/ x  |                                                       
                                                       |x + -------|*|x + -------|                                                       
                                                       |     2    2| |     2    2|                                                       
                                                       \    x  - a / |    x  - a |
((x+re⁡(x−a2+x2))(re⁡(1x(−a2+x2))2−2re⁡(x32(−a2+x2)2)+1)+(im⁡(1x(−a2+x2))2−2im⁡(x32(−a2+x2)2))im⁡(x−a2+x2))sign⁡(x−a2+x2+x)(x−a2+x2+x)∣x−a2+x2+x∣\frac{\left(\left(x + \operatorname{re}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}}\right)}\right) \left(\frac{\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(- a^{2} + x^{2}\right)}\right)}}{2} - 2 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(- a^{2} + x^{2}\right)^{2}}\right)} + 1\right) + \left(\frac{\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(- a^{2} + x^{2}\right)}\right)}}{2} - 2 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(- a^{2} + x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}} + x \right)}}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}} + x\right) \left|{\frac{\sqrt{x}}{- a^{2} + x^{2}} + x}\right|}
Simplificar
Segunda derivada [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 2                    
                                                                                                                                                                                                                                                                                                                                                                                                                                       //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\ /                            3/2  \     /        ___ \   //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\       /        ___ \
                                                                                                                                                                                                                                                                                                                                                                                                                                       ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  || |            1            4*x     |     |      \/ x  |   ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  ||      2|      \/ x  |
                                                                                                                                                                                                                                                                                                                                                                                                                                       ||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*|-2 + --------------- + ----------|*sign|-x + -------|   ||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *sign |-x + -------|
/                                        2                                                2                                                                                                                                                                \                                                                                                                                                                           ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2|| |       ___ / 2    2\            2|     |      2    2|   ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2||       |      2    2|
|/    /    3/2   \                      \    /         /    3/2   \                      \    /                            /    ___   \        /    5/2   \\   /   ___ \   /      /   ___ \\ /                            /    ___   \        /    5/2   \\|     /        ___ \     //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\   /     /        ___ \\   |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /| |     \/ x *\a  - x /   / 2    2\ |     \     a  - x /   |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /|       \     a  - x /
||    |   x      |     /       1       \|    |         |   x      |     /       1       \|    |    /      1       \        |  \/ x    |        |   x      ||   | \/ x  |   |      | \/ x  || |    /      1       \        |  \/ x    |        |   x      |||     |      \/ x  |     ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  || d |     |      \/ x  ||   \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            / \                       \a  - x / /                      \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                     
||4*im|----------| + im|---------------||  + |-2 + 4*re|----------| + re|---------------||  + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||*sign|-x + -------| + 2*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*--|-sign|-x + -------|| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------
||    |         2|     |  ___ / 2    2\||    |         |         2|     |  ___ / 2    2\||    |    | 3/2 / 2    2\|        |         2|        |         3||   | 2    2|   |      | 2    2|| |    | 3/2 / 2    2\|        |         2|        |         3|||     |      2    2|     ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2|| dx|     |      2    2||                                                                                             ___                                                                                                                                             /        ___ \ |        ___ |                                                        
||    |/ 2    2\ |     \\/ x *\a  - x //|    |         |/ 2    2\ |     \\/ x *\a  - x //|    |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ ||   \a  - x /   \      \a  - x // |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ |||     \     a  - x /     |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /|   \     \     a  - x //                                                                                           \/ x                                                                                                                                              |      \/ x  | |      \/ x  |                                                        
\\    \\a  - x / /                      /    \         \\a  - x / /                      /    \                            \\a  - x / /        \\a  - x / //                                 \                            \\a  - x / /        \\a  - x / ///                        \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                                                                                                             -x + -------                                                                                                                                            |-x + -------|*|-x + -------|                                                        
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               2    2                                                                                                                                            |      2    2| |      2    2|                                                        
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              a  - x                                                                                                                                             \     a  - x / |     a  - x |                                                        
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                     /        ___ \ |        ___ |                                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                     |      \/ x  | |      \/ x  |                                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                   4*|-x + -------|*|-x + -------|                                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                     |      2    2| |      2    2|                                                                                                                                                                                                                                                                                                                                                                    
                                                                                                                                                                                                                                                                                                                                                                     \     a  - x / |     a  - x |
2((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))∂∂x(−sign⁡(xa2−x2−x))+(−(x−re⁡(xa2−x2))(−re⁡(1x32(a2−x2))+16re⁡(x(a2−x2)2)+32re⁡(x52(a2−x2)3))+(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))2+(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)2+(−im⁡(1x32(a2−x2))+16im⁡(x(a2−x2)2)+32im⁡(x52(a2−x2)3))im⁡(xa2−x2))sign⁡(xa2−x2−x)−((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))2sign⁡2(xa2−x2−x)(xa2−x2−x)∣xa2−x2−x∣+((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))(4x32(a2−x2)2−2+1x(a2−x2))sign⁡(xa2−x2−x)xa2−x2−x4(xa2−x2−x)∣xa2−x2−x∣\frac{2 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right) + \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)} - \frac{\left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{2} \operatorname{sign}^{2}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} + \frac{\left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}}{4 \left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|}
Simplificar
Tercera derivada [src] 
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                        2                                                2                                                                                                                                                                \                                                                                                                                                3                                                            2                                                                                                                                                                                                                                                                                                                                                                                                                                                                             /                                        2                                                2                                                                                                                                                                \                                                                                                                             2                                                                                                                                                                                     2                                           
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\ /                            3/2  \   /     /        ___ \\     /                            3/2  \ |/    /    3/2   \                      \    /         /    3/2   \                      \    /                            /    ___   \        /    5/2   \\   /   ___ \   /      /   ___ \\ /                            /    ___   \        /    5/2   \\|     /        ___ \     //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\       /        ___ \     /                            3/2  \  //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\     /        ___ \   //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\ /              ___        5/2  \     /        ___ \          /        ___ \ //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\ |/    /    3/2   \                      \    /         /    3/2   \                      \    /                            /    ___   \        /    5/2   \\   /   ___ \   /      /   ___ \\ /                            /    ___   \        /    5/2   \\|     //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\       /        ___ \ /                            3/2  \     //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\    /     /        ___ \\     /        ___ \
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  || |            1            4*x     | d |     |      \/ x  ||     |            1            4*x     | ||    |   x      |     /       1       \|    |         |   x      |     /       1       \|    |    /      1       \        |  \/ x    |        |   x      ||   | \/ x  |   |      | \/ x  || |    /      1       \        |  \/ x    |        |   x      |||     |      \/ x  |     ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  ||      3|      \/ x  |     |            1            4*x     |  ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  ||     |      \/ x  |   ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  || |   1     16*\/ x     32*x     |     |      \/ x  |         2|      \/ x  | ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  || ||    |   x      |     /       1       \|    |         |   x      |     /       1       \|    |    /      1       \        |  \/ x    |        |   x      ||   | \/ x  |   |      | \/ x  || |    /      1       \        |  \/ x    |        |   x      |||     ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  ||      2|      \/ x  | |            1            4*x     |     ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  ||  d |     |      \/ x  ||     |      \/ x  |
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 4*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*|-2 + --------------- + ----------|*--|-sign|-x + -------||   2*|-2 + --------------- + ----------|*||4*im|----------| + im|---------------||  + |-2 + 4*re|----------| + re|---------------||  + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||*sign|-x + -------|   2*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *sign |-x + -------|   2*|-2 + --------------- + ----------| *||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*sign|-x + -------|   ||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*|- ---- + -------- + ----------|*sign|-x + -------|   3*sign |-x + -------|*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*||4*im|----------| + im|---------------||  + |-2 + 4*re|----------| + re|---------------||  + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||   3*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *sign |-x + -------|*|-2 + --------------- + ----------|   6*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *--|-sign|-x + -------||*sign|-x + -------|
    /                                        2                                                2                                                                                                                                                                \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2|| |       ___ / 2    2\            2| dx|     |      2    2||     |       ___ / 2    2\            2| ||    |         2|     |  ___ / 2    2\||    |         |         2|     |  ___ / 2    2\||    |    | 3/2 / 2    2\|        |         2|        |         3||   | 2    2|   |      | 2    2|| |    | 3/2 / 2    2\|        |         2|        |         3|||     |      2    2|     ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2||       |      2    2|     |       ___ / 2    2\            2|  ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2||     |      2    2|   ||      | 2    2|| |         |         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|     |  ___ / 2    2\||    |         |         2|     |  ___ / 2    2\||    |    | 3/2 / 2    2\|        |         2|        |         3||   | 2    2|   |      | 2    2|| |    | 3/2 / 2    2\|        |         2|        |         3|||     ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2||       |      2    2| |       ___ / 2    2\            2|     ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2||  dx|     |      2    2||     |      2    2|
    |/    /    3/2   \                      \    /         /    3/2   \                      \    /                            /    ___   \        /    5/2   \\   /   ___ \   /      /   ___ \\ /                            /    ___   \        /    5/2   \\|   /     /        ___ \\     //    /    3/2   \                      \ /                            /    ___   \        /    5/2   \\   /         /    3/2   \                      \ /                            /    ___   \        /    5/2   \\   /                              /    3/2   \         /    7/2   \                     \   /   ___ \   /      /   ___ \\ /                              /    3/2   \         /    7/2   \                     \\     /        ___ \     //      /   ___ \\ /         /    3/2   \                      \   /    /    3/2   \                      \   /   ___ \\   2/     /        ___ \\     |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /| |     \/ x *\a  - x /   / 2    2\ |   \     \     a  - x //     |     \/ x *\a  - x /   / 2    2\ | ||    |/ 2    2\ |     \\/ x *\a  - x //|    |         |/ 2    2\ |     \\/ x *\a  - x //|    |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ ||   \a  - x /   \      \a  - x // |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ |||     \     a  - x /     |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /|       \     a  - x /     |     \/ x *\a  - x /   / 2    2\ |  |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /|     \     a  - x /   |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /| |  x      a  - x     / 2    2\ |     \     a  - x /          \     a  - x / |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /| ||    |/ 2    2\ |     \\/ x *\a  - x //|    |         |/ 2    2\ |     \\/ x *\a  - x //|    |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ ||   \a  - x /   \      \a  - x // |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ |||     |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /|       \     a  - x / |     \/ x *\a  - x /   / 2    2\ |     |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /|    \     \     a  - x //     \     a  - x /
    ||    |   x      |     /       1       \|    |         |   x      |     /       1       \|    |    /      1       \        |  \/ x    |        |   x      ||   | \/ x  |   |      | \/ x  || |    /      1       \        |  \/ x    |        |   x      ||| d |     |      \/ x  ||     ||    |   x      |     /       1       \| |    /      1       \        |  \/ x    |        |   x      ||   |         |   x      |     /       1       \| |    /      1       \        |  \/ x    |        |   x      ||   |    /       1        \        |   x      |         |   x      |     /      1       \|   | \/ x  |   |      | \/ x  || |    /       1        \        |   x      |         |   x      |     /      1       \||     |      \/ x  |     ||      | \/ x  || |         |   x      |     /       1       \|   |    |   x      |     /       1       \|   | \/ x  ||  d |     |      \/ x  ||     \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            / \                       \a  - x / /                             \                       \a  - x / / \\    \\a  - x / /                      /    \         \\a  - x / /                      /    \                            \\a  - x / /        \\a  - x / //                                 \                            \\a  - x / /        \\a  - x / ///                        \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                          \                       \a  - x / /  \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                      \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            / \                    \a  - x / /                                            \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            / \\    \\a  - x / /                      /    \         \\a  - x / /                      /    \                            \\a  - x / /        \\a  - x / //                                 \                            \\a  - x / /        \\a  - x / ///     \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                      \                       \a  - x / /     \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                                            
- 4*||4*im|----------| + im|---------------||  + |-2 + 4*re|----------| + re|---------------||  + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||*--|-sign|-x + -------|| + 3*||4*im|----------| + im|---------------||*|- im|--------------| + 16*im|----------| + 32*im|----------|| + |-2 + 4*re|----------| + re|---------------||*|- re|--------------| + 16*re|----------| + 32*re|----------|| + |4*im|----------------| + 96*im|----------| + 128*im|----------| + im|--------------||*im|-------| - |x - re|-------||*|4*re|----------------| + 96*re|----------| + 128*re|----------| + re|--------------|||*sign|-x + -------| + 4*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*---|-sign|-x + -------|| - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
    ||    |         2|     |  ___ / 2    2\||    |         |         2|     |  ___ / 2    2\||    |    | 3/2 / 2    2\|        |         2|        |         3||   | 2    2|   |      | 2    2|| |    | 3/2 / 2    2\|        |         2|        |         3||| dx|     |      2    2||     ||    |         2|     |  ___ / 2    2\|| |    | 3/2 / 2    2\|        |         2|        |         3||   |         |         2|     |  ___ / 2    2\|| |    | 3/2 / 2    2\|        |         2|        |         3||   |    |               2|        |         3|         |         4|     | 5/2 / 2    2\||   | 2    2|   |      | 2    2|| |    |               2|        |         3|         |         4|     | 5/2 / 2    2\|||     |      2    2|     ||      | 2    2|| |         |         2|     |  ___ / 2    2\||   |    |         2|     |  ___ / 2    2\||   | 2    2||   2|     |      2    2||                                                                                                ___                                                                                                                                                                                                                                                      ___                                                                                                                                                                                                                              2               2                                                                                                                                                          2                                                                                                                                                                         /        ___ \                                                                                                                                                                                                                                                                    /        ___ \ |        ___ |                                                                                                                                                                                                                                                                                   2                                                                                                                                                                /        ___ \ |        ___ |                                                                     
    ||    |/ 2    2\ |     \\/ x *\a  - x //|    |         |/ 2    2\ |     \\/ x *\a  - x //|    |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ ||   \a  - x /   \      \a  - x // |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ |||   \     \     a  - x //     ||    |/ 2    2\ |     \\/ x *\a  - x //| |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ ||   |         |/ 2    2\ |     \\/ x *\a  - x //| |    \x   *\a  - x //        |/ 2    2\ |        |/ 2    2\ ||   |    |  ___ / 2    2\ |        |/ 2    2\ |         |/ 2    2\ |     \x   *\a  - x //|   \a  - x /   \      \a  - x // |    |  ___ / 2    2\ |        |/ 2    2\ |         |/ 2    2\ |     \x   *\a  - x //||     \     a  - x /     |\      \a  - x // |         |/ 2    2\ |     \\/ x *\a  - x //|   |    |/ 2    2\ |     \\/ x *\a  - x //|   \a  - x /| dx \     \     a  - x //                                                                                              \/ x                                                                                                                                                                                                                                                     \/ x                                                                                                                                                                                                                 /        ___ \  |        ___ |                                                                                                                                             /        ___ \                                                                                                                                                                / 2    2\ |      \/ x  |                                                                                                                                                                                                                                                                    |      \/ x  | |      \/ x  |                                                                                                                                                                                                                                                                     /        ___ \  |        ___ |                                                                                                                                                 |      \/ x  | |      \/ x  |                                                                     
    \\    \\a  - x / /                      /    \         \\a  - x / /                      /    \                            \\a  - x / /        \\a  - x / //                                 \                            \\a  - x / /        \\a  - x / ///                             \\    \\a  - x / /                      / \                            \\a  - x / /        \\a  - x / //   \         \\a  - x / /                      / \                            \\a  - x / /        \\a  - x / //   \    \\/ x *\a  - x / /        \\a  - x / /         \\a  - x / /                     /                                 \    \\/ x *\a  - x / /        \\a  - x / /         \\a  - x / /                     //                        \                  \         \\a  - x / /                      /   \    \\a  - x / /                      /            /                                                                                                                 -x + -------                                                                                                                                                                                                                                             -x + -------                                                                                                                                                                                                               |      \/ x  |  |      \/ x  |                                                                                                                                             |      \/ x  |                                                                                                                                                                \a  - x /*|-x + -------|                                                                                                                                                                                                                                                                    |-x + -------|*|-x + -------|                                                                                                                                                                                                                                                                     |      \/ x  |  |      \/ x  |                                                                                                                                                 |-x + -------|*|-x + -------|                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2    2                                                                                                                                                                                                                                                   2    2                                                                                                                                                                                                               |-x + -------| *|-x + -------|                                                                                                                                             |-x + -------|                                                                                                                                                                          |      2    2|                                                                                                                                                                                                                                                                    |      2    2| |      2    2|                                                                                                                                                                                                                                                                     |-x + -------| *|-x + -------|                                                                                                                                                 |      2    2| |      2    2|                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                           a  - x                                                                                                                                                                                                                                                   a  - x                                                                                                                                                                                                                |      2    2|  |      2    2|                                                                                                                                             |      2    2|                                                                                                                                                                          \     a  - x /                                                                                                                                                                                                                                                                    \     a  - x / |     a  - x |                                                                                                                                                                                                                                                                     |      2    2|  |      2    2|                                                                                                                                                 \     a  - x / |     a  - x |                                                                     
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                          \     a  - x /  |     a  - x |                                                                                                                                             \     a  - x /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                              \     a  - x /  |     a  - x |                                                                                                                                                                                                                                                   
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   /        ___ \ |        ___ |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |      \/ x  | |      \/ x  |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 8*|-x + -------|*|-x + -------|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   |      2    2| |      2    2|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \     a  - x / |     a  - x |
4((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))∂2∂x2(−sign⁡(xa2−x2−x))−4(−(x−re⁡(xa2−x2))(−re⁡(1x32(a2−x2))+16re⁡(x(a2−x2)2)+32re⁡(x52(a2−x2)3))+(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))2+(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)2+(−im⁡(1x32(a2−x2))+16im⁡(x(a2−x2)2)+32im⁡(x52(a2−x2)3))im⁡(xa2−x2))∂∂x(−sign⁡(xa2−x2−x))+3(−(x−re⁡(xa2−x2))(re⁡(1x52(a2−x2))+4re⁡(1x(a2−x2)2)+96re⁡(x32(a2−x2)3)+128re⁡(x72(a2−x2)4))+(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))(−im⁡(1x32(a2−x2))+16im⁡(x(a2−x2)2)+32im⁡(x52(a2−x2)3))+(−re⁡(1x32(a2−x2))+16re⁡(x(a2−x2)2)+32re⁡(x52(a2−x2)3))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)+(im⁡(1x52(a2−x2))+4im⁡(1x(a2−x2)2)+96im⁡(x32(a2−x2)3)+128im⁡(x72(a2−x2)4))im⁡(xa2−x2))sign⁡(xa2−x2−x)+6((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))2sign⁡(xa2−x2−x)∂∂x(−sign⁡(xa2−x2−x))(xa2−x2−x)∣xa2−x2−x∣−4((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))(4x32(a2−x2)2−2+1x(a2−x2))∂∂x(−sign⁡(xa2−x2−x))xa2−x2−x+3((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))(−(x−re⁡(xa2−x2))(−re⁡(1x32(a2−x2))+16re⁡(x(a2−x2)2)+32re⁡(x52(a2−x2)3))+(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))2+(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)2+(−im⁡(1x32(a2−x2))+16im⁡(x(a2−x2)2)+32im⁡(x52(a2−x2)3))im⁡(xa2−x2))sign⁡2(xa2−x2−x)(xa2−x2−x)∣xa2−x2−x∣−2(4x32(a2−x2)2−2+1x(a2−x2))(−(x−re⁡(xa2−x2))(−re⁡(1x32(a2−x2))+16re⁡(x(a2−x2)2)+32re⁡(x52(a2−x2)3))+(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))2+(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)2+(−im⁡(1x32(a2−x2))+16im⁡(x(a2−x2)2)+32im⁡(x52(a2−x2)3))im⁡(xa2−x2))sign⁡(xa2−x2−x)xa2−x2−x−2((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))3sign⁡3(xa2−x2−x)(xa2−x2−x)2∣xa2−x2−x∣2+3((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))2(4x32(a2−x2)2−2+1x(a2−x2))sign⁡2(xa2−x2−x)(xa2−x2−x)2∣xa2−x2−x∣−2((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))(4x32(a2−x2)2−2+1x(a2−x2))2sign⁡(xa2−x2−x)(xa2−x2−x)2+((x−re⁡(xa2−x2))(re⁡(1x(a2−x2))+4re⁡(x32(a2−x2)2)−2)−(im⁡(1x(a2−x2))+4im⁡(x32(a2−x2)2))im⁡(xa2−x2))(32x52(a2−x2)2+16xa2−x2−1x32)sign⁡(xa2−x2−x)(a2−x2)(xa2−x2−x)8(xa2−x2−x)∣xa2−x2−x∣\frac{4 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \frac{\partial^{2}}{\partial x^{2}} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right) - 4 \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right) + 3 \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{x^{\frac{5}{2}} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)^{2}}\right)} + 96 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)} + 128 \operatorname{re}{\left(\frac{x^{\frac{7}{2}}}{\left(a^{2} - x^{2}\right)^{4}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) + \left(\operatorname{im}{\left(\frac{1}{x^{\frac{5}{2}} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)^{2}}\right)} + 96 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)} + 128 \operatorname{im}{\left(\frac{x^{\frac{7}{2}}}{\left(a^{2} - x^{2}\right)^{4}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)} + \frac{6 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{2} \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)} \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right)}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} - \frac{4 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right)}{\frac{\sqrt{x}}{a^{2} - x^{2}} - x} + \frac{3 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}^{2}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} - \frac{2 \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\frac{\sqrt{x}}{a^{2} - x^{2}} - x} - \frac{2 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{3} \operatorname{sign}^{3}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)^{2} \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|^{2}} + \frac{3 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{2} \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \operatorname{sign}^{2}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)^{2} \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} - \frac{2 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)^{2} \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)^{2}} + \frac{\left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{32 x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{2}} + \frac{16 \sqrt{x}}{a^{2} - x^{2}} - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(a^{2} - x^{2}\right) \left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)}}{8 \left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|}
Simplificar
    © Sr Examen – Калькулятор