Sr Examen
Otras calculadoras
- Derivada de una función implícitamente dada
- Derivada de una función paramétrica
- Derivada parcial de la función
- Análisis de la función gráfica
- Integrales paso a paso
- Ecuaciones diferenciales paso a paso
- Límites paso por paso
-
¿Cómo usar?
- Derivada de:
-
Derivada de x^(3*x)
-
Derivada de x^3*sin(x)
-
Derivada de √x
-
Derivada de e^x+x^2
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Expresiones idénticas
- |x+sqrt(x^ dos -a^ dos)|
- módulo de x más raíz cuadrada de (x al cuadrado menos a al cuadrado )|
- módulo de x más raíz cuadrada de (x en el grado dos menos a en el grado dos)|
- |x+√(x^2-a^2)|
- |x+sqrt(x2-a2)|
- |x+sqrtx2-a2|
- |x+sqrt(x²-a²)|
- |x+sqrt(x en el grado 2-a en el grado 2)|
- |x+sqrtx^2-a^2|
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Expresiones semejantes
- |x+sqrt(x^2+a^2)|
- |x-sqrt(x^2-a^2)|
-
Expresiones con funciones
- Raíz cuadrada sqrt
- sqrt
- sqrt3x
- sqrt(3*x)
- sqrt(x)^2
- sqrt(x)+3*x^3
- Módulo |
- |x|*(x+1)
- |x|*e^(-|x-1|)
- |(x^2)+(3*x)-4|
- |z−3i|
- |y|+pi/4
Derivada de |x+sqrt(x^2-a^2)|
Solución
Ha introducido
[src]
| _________| | / 2 2 | |x + \/ x - a |
$$\left|{x + \sqrt{- a^{2} + x^{2}}}\right|$$
Abs(x + sqrt(x^2 - a^2))
Primera derivada
[src]
/ / / / 2 2 2 \\ / / 2 2 2 \\\ / / / 2 2 2 \\ / / 2 2 2 \\ \ \
|/ ___________________________________________ \ | / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| ___________________________________________ | / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | |
|| / 2 / / 2 2 2 \\| | x*\x + im (a) - re (a)/*cos|-------------------------------------------| 2*x*im(a)*re(a)*sin|-------------------------------------------|| / 2 |x*\x + im (a) - re (a)/*sin|-------------------------------------------| 2*x*cos|-------------------------------------------|*im(a)*re(a)| / / 2 2 2 \\| / _________\
|| 4 / / 2 2 2 \ 2 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| | \ 2 / \ 2 /| 4 / / 2 2 2 \ 2 2 | \ 2 / \ 2 / | |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| | / 2 2 |
||x + \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) *cos|-------------------------------------------||*|1 + ------------------------------------------------------------------------- - ----------------------------------------------------------------| + \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) *|------------------------------------------------------------------------- + ----------------------------------------------------------------|*sin|-------------------------------------------||*sign\x + \/ x - a /
|\ \ 2 // | 3/4 3/4 | | 3/4 3/4 | \ 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 | | |
\ \ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ / \ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ / /
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_________
/ 2 2
x + \/ x - a
$$\frac{\left(\left(x + \sqrt[4]{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(\frac{x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} - \frac{2 x \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} + 1\right) + \left(\frac{x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} + \frac{2 x \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}}\right) \sqrt[4]{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \operatorname{sign}{\left(x + \sqrt{- a^{2} + x^{2}} \right)}}{x + \sqrt{- a^{2} + x^{2}}}$$
Segunda derivada
[src]
/ / / / 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 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| |/ 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | |atan2\-2*im(a)*re(a), x + im (a) - re (a)/||
| / ___________________________________________ \ | 2 / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 2 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| | 2 / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 2 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | | || / 2 / / 2 2 2 \\| | x*\x + im (a) - re (a)/*cos|-------------------------------------------| 2*x*im(a)*re(a)*sin|-------------------------------------------|| x*|\x + im (a) - re (a)/*sin|-------------------------------------------| + 2*cos|-------------------------------------------|*im(a)*re(a)|*sin|-------------------------------------------|| / _________\
| | / 2 / / 2 2 2 \\| | / / 2 2 2 \\ / / 2 2 2 \\ / / 2 2 2 \\ 3*x *\x + im (a) - re (a)/ *cos|-------------------------------------------| 4*x *im (a)*re (a)*cos|-------------------------------------------| 4*x *\x + im (a) - re (a)/*im(a)*re(a)*sin|-------------------------------------------|| | / / 2 2 2 \\ / / 2 2 2 \\ / / 2 2 2 \\ 3*x *\x + im (a) - re (a)/ *sin|-------------------------------------------| 4*x *im (a)*re (a)*sin|-------------------------------------------| 4*x *\x + im (a) - re (a)/*cos|-------------------------------------------|*im(a)*re(a)| / / 2 2 2 \\ | / x \ || 4 / / 2 2 2 \ 2 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| | / 2 2 |
| 2 | 4 / / 2 2 2 \ 2 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| |/ 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| \ 2 / \ 2 / \ 2 /| |/ 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| \ 2 / \ 2 / \ 2 / | |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | |1 + ------------|*||x + \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) *cos|-------------------------------------------||*|1 + ------------------------------------------------------------------------- - ----------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/ x - a /
/ / / / 2 2 2 \\ / / 2 2 2 \\\ / / / 2 2 2 \\ / / 2 2 2 \\ \ / / 2 2 2 \\\ |/ / / 2 2 2 \\ / / 2 2 2 \\\ |x + \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) *cos|-------------------------------------------||*|\x + im (a) - re (a)/*cos|-------------------------------------------| + 2*x *cos|-------------------------------------------| - 2*im(a)*re(a)*sin|-------------------------------------------| - ----------------------------------------------------------------------------- - ------------------------------------------------------------------- + ----------------------------------------------------------------------------------------| |\x + im (a) - re (a)/*sin|-------------------------------------------| + 2*x *sin|-------------------------------------------| + 2*cos|-------------------------------------------|*im(a)*re(a) - ----------------------------------------------------------------------------- - ------------------------------------------------------------------- - ----------------------------------------------------------------------------------------|*sin|-------------------------------------------| / / / 2 2 2 \\ / / 2 2 2 \\ \ / / 2 2 2 \\ / / / 2 2 2 \\ / / 2 2 2 \\ \ / / 2 2 2 \\ | | _________| |\ \ 2 // | 3/4 3/4 | ___________________________________________ |
|/ ___________________________________________ \ | / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| |/ 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| || / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| \ \ 2 // | \ 2 / \ 2 / \ 2 / 2 2 2 | | \ 2 / \ 2 / \ 2 / 2 2 2 | \ 2 / 2 |/ 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | / 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| 2 |/ 2 2 2 \ |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | |atan2\-2*im(a)*re(a), x + im (a) - re (a)/| | | / 2 2 | | | / 2 \ / 2 \ | / 2 |
|| / 2 / / 2 2 2 \\| | x*\x + im (a) - re (a)/*cos|-------------------------------------------| 2*x*im(a)*re(a)*sin|-------------------------------------------|| x*|\x + im (a) - re (a)/*sin|-------------------------------------------| + 2*cos|-------------------------------------------|*im(a)*re(a)|*sin|-------------------------------------------|| / / _________\\ || x*\x + im (a) - re (a)/*cos|-------------------------------------------| 2*x*im(a)*re(a)*sin|-------------------------------------------|| | / 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 | x *|\x + im (a) - re (a)/*sin|-------------------------------------------| + 2*cos|-------------------------------------------|*im(a)*re(a)|*\x + im (a) - re (a)/*sin|-------------------------------------------| 2*x *|\x + im (a) - re (a)/*sin|-------------------------------------------| + 2*cos|-------------------------------------------|*im(a)*re(a)|*cos|-------------------------------------------|*im(a)*re(a)| / _________\ \ \/ x - a / | | |/ 2 2 2 \ 2 2 | |/ 2 2 2 \ 2 2 | | / / 2 2 2 \ 2 2 |
|| 4 / / 2 2 2 \ 2 2 |atan2\-2*im(a)*re(a), x + im (a) - re (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| d | | / 2 2 || || \ 2 / \ 2 /| \ \x + im (a) - re (a)/ + 4*im (a)*re (a) \x + im (a) - re (a)/ + 4*im (a)*re (a) \x + im (a) - re (a)/ + 4*im (a)*re (a) / \ \x + im (a) - re (a)/ + 4*im (a)*re (a) \x + im (a) - re (a)/ + 4*im (a)*re (a) \x + im (a) - re (a)/ + 4*im (a)*re (a) / \ \ 2 / \ 2 / / \ 2 / \ \ 2 / \ 2 / / \ 2 / | | / 2 2 | \ \ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ / \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) /
||x + \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) *cos|-------------------------------------------||*|1 + ------------------------------------------------------------------------- - ----------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*--\sign\x + \/ x - a // + ||1 + ------------------------------------------------------------------------- - ----------------------------------------------------------------| + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/ x - a / - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
|\ \ 2 // | 3/4 3/4 | ___________________________________________ | dx || 3/4 3/4 | 3/4 ___________________________________________ 3/2 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 2 \ 2 2 | / / 2 2 2 \ 2 2 |/ 2 2 2 \ 2 2 | |/ 2 2 2 \ 2 2 | | x + \/ x - a
\ \ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ / \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) / \\ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ / \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \/ \x + im (a) - re (a)/ + 4*im (a)*re (a) \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ \\x + im (a) - re (a)/ + 4*im (a)*re (a)/ /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
_________
/ 2 2
x + \/ x - a
$$\frac{\left(\frac{x \left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 2 \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\sqrt{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}} + \left(x + \sqrt[4]{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(\frac{x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} - \frac{2 x \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} + 1\right)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \sqrt{- a^{2} + x^{2}} \right)} + \left(\frac{x^{2} \left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 2 \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{2}}} + \frac{2 x^{2} \left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 2 \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{2}}} + \frac{\left(x + \sqrt[4]{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(2 x^{2} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \frac{3 x^{2} \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \frac{4 x^{2} \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{4 x^{2} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - 2 \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right)}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} + \left(\frac{x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} - \frac{2 x \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} + 1\right)^{2} + \frac{\left(2 x^{2} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} - \frac{3 x^{2} \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{4 x^{2} \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} - \frac{4 x^{2} \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 2 \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\sqrt{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}}\right) \operatorname{sign}{\left(x + \sqrt{- a^{2} + x^{2}} \right)} - \frac{\left(\frac{x}{\sqrt{- a^{2} + x^{2}}} + 1\right) \left(\frac{x \left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} + 2 \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}\right) \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\sqrt{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}}} + \left(x + \sqrt[4]{\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}} \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}\right) \left(\frac{x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \cos{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} - \frac{2 x \sin{\left(\frac{\operatorname{atan_{2}}{\left(- 2 \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)},x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2} \right)}}{2} \right)} \operatorname{re}{\left(a\right)} \operatorname{im}{\left(a\right)}}{\left(\left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} + 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{\frac{3}{4}}} + 1\right)\right) \operatorname{sign}{\left(x + \sqrt{- a^{2} + x^{2}} \right)}}{x + \sqrt{- a^{2} + x^{2}}}}{x + \sqrt{- a^{2} + x^{2}}}$$