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:
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Derivada de 2*cos(3*x)
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Derivada de x^(7/6)
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Derivada de x^(2/5)
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Derivada de 1/ln(x)
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Expresiones idénticas
- x*ln|x+sqrt(x^ dos +a^ dos)|exp(-x)
- x multiplicar por ln módulo de x más raíz cuadrada de (x al cuadrado más a al cuadrado )| exponente de ( menos x)
- x multiplicar por ln módulo de x más raíz cuadrada de (x en el grado dos más a en el grado dos)| exponente de ( menos x)
- x*ln|x+√(x^2+a^2)|exp(-x)
- x*ln|x+sqrt(x2+a2)|exp(-x)
- x*ln|x+sqrtx2+a2|exp-x
- x*ln|x+sqrt(x²+a²)|exp(-x)
- x*ln|x+sqrt(x en el grado 2+a en el grado 2)|exp(-x)
- xln|x+sqrt(x^2+a^2)|exp(-x)
- xln|x+sqrt(x2+a2)|exp(-x)
- xln|x+sqrtx2+a2|exp-x
- xln|x+sqrtx^2+a^2|exp-x
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Expresiones semejantes
- x*ln|x+sqrt(x^2-a^2)|exp(-x)
- x*ln|x-sqrt(x^2+a^2)|exp(-x)
- x*ln|x+sqrt(x^2+a^2)|exp(x)
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Expresiones con funciones
- ln
- ln(√x)
- ln(x+1)/x^2
- ln(x^1/2)
- ln(tgx/2)
- ln(tg(2x))
- Raíz cuadrada sqrt
- sqrt(x)^3+1
- sqrt(x)*i^n*(sqrt(x)+sqrt(x+1))
- sqrt5x
- sqrt(x)-cos(x)+2
- sqrt(x)*asin(sqrt(x))+sqrt(1-x)
- Módulo |
- |x+3|
- |z|*z
- |x|^(π)
- |x|*x*a
- |x*x-5*x|
Derivada de x*ln|x+sqrt(x^2+a^2)|exp(-x)
Solución
Ha introducido
[src]
/| _________|\
|| / 2 2 || -x
x*log\|x + \/ x + a |/*e
$$x \log{\left(\left|{x + \sqrt{a^{2} + x^{2}}}\right| \right)} e^{- x}$$
(x*log(Abs(x + sqrt(x^2 + a^2))))*exp(-x)
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 + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| ___________________________________________ | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | | | | || / 2 / / 2 2 2 \\| | x*\x + re (a) - im (a)/*cos|------------------------------------------| 2*x*im(a)*re(a)*sin|------------------------------------------|| / 2 |x*\x + re (a) - im (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 + re (a) - im (a)/|| | \ 2 / \ 2 /| 4 / / 2 2 2 \ 2 2 | \ 2 / \ 2 / | |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | / 2 2 | | |x*||x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *|------------------------------------------------------------------------ - ---------------------------------------------------------------|*sin|------------------------------------------||*sign\x + \/ a + x / | | |\ \ 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 + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / / || / 2 2 ||| -x -x || / 2 2 || |-------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + log\|x + \/ x + a |/|*e - x*e *log\|x + \/ x + a |/ | / _________\ | _________| | | | / 2 2 | | / 2 2 | | \ \x + \/ a + x /*|x + \/ x + a | /
$$- x e^{- x} \log{\left(\left|{x + \sqrt{a^{2} + x^{2}}}\right| \right)} + \left(\frac{x \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)}}{\left(x + \sqrt{a^{2} + x^{2}}\right) \left|{x + \sqrt{a^{2} + x^{2}}}\right|} + \log{\left(\left|{x + \sqrt{a^{2} + x^{2}}}\right| \right)}\right) e^{- x}$$
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 \\ / / 2 2 2 \\\ / 2 / / 2 2 2 \\ / / 2 2 2 \\ / / 2 2 2 \\ \ \ |/ ___________________________________________ \ | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ ___________________________________________ \ | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | | | | | / ___________________________________________ \ | 2 / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | 2 / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | | || / 2 / / 2 2 2 \\| | x*\x + re (a) - im (a)/*cos|------------------------------------------| 2*x*im(a)*re(a)*sin|------------------------------------------|| x*|\x + re (a) - im (a)/*sin|------------------------------------------| - 2*cos|------------------------------------------|*im(a)*re(a)|*sin|------------------------------------------|| / _________\ || / 2 / / 2 2 2 \\| | x*\x + re (a) - im (a)/*cos|------------------------------------------| 2*x*im(a)*re(a)*sin|------------------------------------------|| x*|\x + re (a) - im (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 + re (a) - im (a)/ *cos|------------------------------------------| 4*x *im (a)*re (a)*cos|------------------------------------------| 4*x *\x + re (a) - im (a)/*im(a)*re(a)*sin|------------------------------------------|| | / / 2 2 2 \\ / / 2 2 2 \\ / / 2 2 2 \\ 3*x *\x + re (a) - im (a)/ *sin|------------------------------------------| 4*x *im (a)*re (a)*sin|------------------------------------------| 4*x *\x + re (a) - im (a)/*cos|------------------------------------------|*im(a)*re(a)| / / 2 2 2 \\ | || 4 / / 2 2 2 \ 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| 2| / 2 2 | / x \ || 4 / / 2 2 2 \ 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| | / 2 2 || | | | | 2 | 4 / / 2 2 2 \ 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| \ 2 / \ 2 / \ 2 /| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| \ 2 / \ 2 / \ 2 / | |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | ||x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| *sign \x + \/ a + x / |1 + ------------|*||x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/ a + x /| | | |/ / / / 2 2 2 \\ / / 2 2 2 \\\ / / / 2 2 2 \\ / / 2 2 2 \\ \ / / 2 2 2 \\\ |/ / / 2 2 2 \\ / / 2 2 2 \\\ |x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|\x + re (a) - im (a)/*cos|------------------------------------------| + 2*x *cos|------------------------------------------| + 2*im(a)*re(a)*sin|------------------------------------------| - ---------------------------------------------------------------------------- - ------------------------------------------------------------------ - ---------------------------------------------------------------------------------------| |\x + re (a) - im (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 // | 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 2 2 \\ \ / / 2 2 2 \\\ | | ||/ ___________________________________________ \ | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| || / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (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 + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| 2 |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | | | / 2 \ / 2 \ | / 2 | | / 2 2 | | | / 2 \ / 2 \ | / 2 | | |/ ___________________________________________ \ | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ ___________________________________________ \ | / 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| |/ 2 2 2 \ |atan2\2*im(a)*re(a), x + re (a) - im (a)/| |atan2\2*im(a)*re(a), x + re (a) - im (a)/| | |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | | ||| / 2 / / 2 2 2 \\| | x*\x + re (a) - im (a)/*cos|------------------------------------------| 2*x*im(a)*re(a)*sin|------------------------------------------|| x*|\x + re (a) - im (a)/*sin|------------------------------------------| - 2*cos|------------------------------------------|*im(a)*re(a)|*sin|------------------------------------------|| / / _________\\ || x*\x + re (a) - im (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 + re (a) - im (a)/*sin|------------------------------------------| - 2*cos|------------------------------------------|*im(a)*re(a)|*\x + re (a) - im (a)/*sin|------------------------------------------| 2*x *|\x + re (a) - im (a)/*sin|------------------------------------------| - 2*cos|------------------------------------------|*im(a)*re(a)|*cos|------------------------------------------|*im(a)*re(a)| / _________\ | | |/ 2 2 2 \ 2 2 | |/ 2 2 2 \ 2 2 | | / / 2 2 2 \ 2 2 | \ \/ a + x / | | |/ 2 2 2 \ 2 2 | |/ 2 2 2 \ 2 2 | | / / 2 2 2 \ 2 2 | | || / 2 / / 2 2 2 \\| | x*\x + re (a) - im (a)/*cos|------------------------------------------| 2*x*im(a)*re(a)*sin|------------------------------------------|| x*|\x + re (a) - im (a)/*sin|------------------------------------------| - 2*cos|------------------------------------------|*im(a)*re(a)|*sin|------------------------------------------|| / _________\ || / 2 / / 2 2 2 \\| | x*\x + re (a) - im (a)/*cos|------------------------------------------| 2*x*im(a)*re(a)*sin|------------------------------------------|| x*|\x + re (a) - im (a)/*sin|------------------------------------------| - 2*cos|------------------------------------------|*im(a)*re(a)|*sin|------------------------------------------|| / _________\| | ||| 4 / / 2 2 2 \ 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| d | | / 2 2 || || \ 2 / \ 2 /| \ \x + re (a) - im (a)/ + 4*im (a)*re (a) \x + re (a) - im (a)/ + 4*im (a)*re (a) \x + re (a) - im (a)/ + 4*im (a)*re (a) / \ \x + re (a) - im (a)/ + 4*im (a)*re (a) \x + re (a) - im (a)/ + 4*im (a)*re (a) \x + re (a) - im (a)/ + 4*im (a)*re (a) / \ \ 2 / \ 2 / / \ 2 / \ \ 2 / \ 2 / / \ 2 / | | / 2 2 | \ \ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) / \ \ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) / | || 4 / / 2 2 2 \ 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| | / 2 2 | || 4 / / 2 2 2 \ 2 2 |atan2\2*im(a)*re(a), x + re (a) - im (a)/|| | \ 2 / \ 2 /| \ \ 2 / \ 2 / / \ 2 /| | / 2 2 || | x*|||x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*--\sign\x + \/ a + x // + ||1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/ a + x / - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------| + 2*||x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/ a + x / 2*x*||x + \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) *cos|------------------------------------------||*|1 + ------------------------------------------------------------------------ + ---------------------------------------------------------------| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*sign\x + \/ a + x /| | ||\ \ 2 // | 3/4 3/4 | ___________________________________________ | dx || 3/4 3/4 | 3/4 ___________________________________________ 3/2 3/2 | / _________\ | _________| _________ | |\ \ 2 // | 3/4 3/4 | ___________________________________________ | |\ \ 2 // | 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 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 + \/ a + x /*|x + \/ a + x | x + \/ a + 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 2 | | | || / 2 2 || || / 2 2 || \\ \ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) / \\ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / / \ \ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) / \ \ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ \\x + re (a) - im (a)/ + 4*im (a)*re (a)/ / \/ \x + re (a) - im (a)/ + 4*im (a)*re (a) / | -x |- 2*log\|x + \/ a + x |/ + x*log\|x + \/ a + x |/ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|*e | / _________\ | _________| / _________\ | _________| | | | / 2 2 | | / 2 2 | | / 2 2 | | / 2 2 | | \ \x + \/ a + x /*|x + \/ a + x | \x + \/ a + x /*|x + \/ a + x | /
$$\left(x \log{\left(\left|{x + \sqrt{a^{2} + x^{2}}}\right| \right)} - \frac{2 x \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)}}{\left(x + \sqrt{a^{2} + x^{2}}\right) \left|{x + \sqrt{a^{2} + x^{2}}}\right|} - 2 \log{\left(\left|{x + \sqrt{a^{2} + x^{2}}}\right| \right)} + \frac{x \left(\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}}} - \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)^{2} \operatorname{sign}^{2}{\left(x + \sqrt{a^{2} + x^{2}} \right)}}{\left(x + \sqrt{a^{2} + x^{2}}\right) \left|{x + \sqrt{a^{2} + x^{2}}}\right|}\right) + 2 \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)}}{\left(x + \sqrt{a^{2} + x^{2}}\right) \left|{x + \sqrt{a^{2} + x^{2}}}\right|}\right) e^{- x}$$