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^(7/6)
-
Derivada de x^-7
-
Derivada de 5*tan(x)^3+sin(4*x)*e^((-x)/7)
-
Derivada de 25/x
-
Expresiones idénticas
- y=ln|x+sqr(x^ dos -a^ dos)|
- y es igual a ln módulo de x más sqr(x al cuadrado menos a al cuadrado )|
- y es igual a ln módulo de x más sqr(x en el grado dos menos a en el grado dos)|
- y=ln|x+sqr(x2-a2)|
- y=ln|x+sqrx2-a2|
- y=ln|x+sqr(x²-a²)|
- y=ln|x+sqr(x en el grado 2-a en el grado 2)|
- y=ln|x+sqrx^2-a^2|
-
Expresiones semejantes
- y=ln|x+sqr(x^2+a^2)|
- y=ln|x-sqr(x^2-a^2)|
-
Expresiones con funciones
- ln
- ln(x/5)
- ln(e^(2*x)+1)
- ln(ax)
- ln(x+sqrt(a^2+x^2))
- ln(3x²)
- sqr
- sqrt(x^3)+4*x^7-2*x
- sqrt(x)/(1+sqrt(x))
- sqrt(5)*sqrt(t)+sqrt(7)/t
- sqrtcos4x
- sqrt(2)*pi*sin(pi*x/4)
- Módulo |
- |z|*rez
- |z|^2+2*z
- |z|^2+2z
- |x|^(π)(x-1)
- |x|*x+3*|x|-5*x
Derivada de y=ln|x+sqr(x^2-a^2)|
Solución
Ha introducido
[src]
/| 2|\ || / 2 2\ || log\|x + \x - a / |/
$$\log{\left(\left|{x + \left(- a^{2} + x^{2}\right)^{2}}\right| \right)}$$
log(Abs(x + (x^2 - a^2)^2))
Primera derivada
[src]
/ / 2 \ \ / 2\
|/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | 2 2 / 2 2 2 \| | / 2 2\ |
\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*sign\x + \x - a / /
---------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ | 2|
| / 2 2\ | | / 2 2\ |
\x + \x - a / /*|x + \x - a / |
$$\frac{\left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)^{2} - 4 \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(- a^{2} + x^{2}\right)^{2} \right)}}{\left(x + \left(- a^{2} + x^{2}\right)^{2}\right) \left|{x + \left(- a^{2} + x^{2}\right)^{2}}\right|}$$
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 2 2 \| d | | / 2 2\ || |/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | / 2 2 2\ 2 2 / 2 2 2 \ 2 2 2 | | / 2 2\ | \-1 + 4*x*\a - x //*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*sign\x + \a - x / / \\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)// *sign \x + \a - x / /
\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*--\sign\x + \a - x / // + \\1 + 4*x*\x + im (a) - re (a)// + 4*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x + im (a) - re (a)/ + 64*x *im (a)*re (a)/*sign\x + \a - x / / + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - -----------------------------------------------------------------------------------------------------------------------------------------------------
dx 2 / 2\ | 2|
/ 2 2\ | / 2 2\ | | / 2 2\ |
x + \a - x / \x + \a - x / /*|x + \a - x / |
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ | 2|
| / 2 2\ | | / 2 2\ |
\x + \a - x / /*|x + \a - x / |
$$\frac{\left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \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) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + \frac{\left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} - \frac{\left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right)^{2} \operatorname{sign}^{2}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|}$$
Tercera derivada
[src]
2
/ / 2 \ \ / / 2\\ 3 / / 2 \ \ / / 2\\ / 2\ 2
2 / / 2 \ \ / 2\ / / 2 2\\ |/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | 2 2 / 2 2 2 \| d | | / 2 2\ || / 2 / 2 \ \ / 2\ / / 2 \ \ / 2\ / / 2 \ \ / 2\ |/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | 2 2 / 2 2 2 \| d | | / 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*\-1 + 4*x*\a - x //*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*--\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 | | / 2 2\ | |/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | 2 2 / 2 2 2 \| 3| / 2 2\ | / 2 2\ |/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | 2 2 / 2 2 2 \| | / 2 2\ | 3*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)// *--\sign\x + \a - x / //*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 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 \| d | | / 2 2\ || |/ / 2 2 2 \\ | / 2 2 2 \ 2 2 | / 2 2 2\ 2 2 / 2 2 2 \ 2 2 2 | d | | / 2 2\ || |/ / 2 2 2 \\ / 2 2 2\ | / 2 2 2 \ 2 2 | 2 2 | | / 2 2\ | 2*\-1 + 4*x*\a - x // *\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*sign\x + \a - x / / dx 2*\-1 + 4*x*\a - x //*\\1 + 4*x*\x + im (a) - re (a)// + 4*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x + im (a) - re (a)/ + 64*x *im (a)*re (a)/*sign\x + \a - x / / 2*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)// *sign \x + \a - x / / 4*\a - 3*x /*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*sign\x + \a - x / / dx 3*sign \x + \a - x / /*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*\\1 + 4*x*\x + im (a) - re (a)// + 4*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x + im (a) - re (a)/ + 64*x *im (a)*re (a)/ 3*\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)// *sign \x + \a - x / /*\-1 + 4*x*\a - x //
\\1 + 4*x*\x + im (a) - re (a)//*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 32*x*im (a)*re (a)*\x + im (a) - re (a)//*---\sign\x + \a - x / // + 2*\\1 + 4*x*\x + im (a) - re (a)// + 4*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/*\im (a) - re (a) + 3*x / + 32*im (a)*re (a)*\x + im (a) - re (a)/ + 64*x *im (a)*re (a)/*--\sign\x + \a - x / // + 12*\\1 + 4*x*\x + im (a) - re (a)//*\im (a) - re (a) + 3*x / + 2*x*\x + \x + im (a) - re (a)/ - 4*im (a)*re (a)/ + 16*x*im (a)*re (a)/*sign\x + \a - x / / + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------
2 dx 2 2 2 2 2 2 / 2\ | 2| / 2\ | 2| 2
dx / 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 / | / 2 2\ | | / 2 2\ | x + \a - x / \x + \a - x / /*|x + \a - x / | \x + \a - x / /*|x + \a - x / | | / 2 2\ | | / 2 2\ |
\x + \a - x / / \x + \a - x / / *|x + \a - x / | \x + \a - x / / *|x + \a - x / |
------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ 2\ | 2|
| / 2 2\ | | / 2 2\ |
\x + \a - x / /*|x + \a - x / |
$$\frac{\frac{4 \left(a^{2} - 3 x^{2}\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} + \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \frac{\partial^{2}}{\partial x^{2}} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + 12 \left(2 x \left(x + \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) + 16 x \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + 2 \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \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) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} + \frac{2 \left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} + \frac{2 \left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \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) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{x + \left(a^{2} - x^{2}\right)^{2}} - \frac{3 \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right)^{2} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)} \frac{\partial}{\partial x} \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|} - \frac{3 \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \left(64 x^{2} \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right)^{2} + 4 \left(x + \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) \left(3 x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 32 \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \operatorname{sign}^{2}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|} + \frac{2 \left(4 x \left(a^{2} - x^{2}\right) - 1\right)^{2} \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right) \operatorname{sign}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right)^{2}} - \frac{3 \left(4 x \left(a^{2} - x^{2}\right) - 1\right) \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right)^{2} \operatorname{sign}^{2}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right)^{2} \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|} + \frac{2 \left(32 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) \left(\operatorname{re}{\left(a\right)}\right)^{2} \left(\operatorname{im}{\left(a\right)}\right)^{2} + \left(4 x \left(x^{2} - \left(\operatorname{re}{\left(a\right)}\right)^{2} + \left(\operatorname{im}{\left(a\right)}\right)^{2}\right) + 1\right) \left(x + \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)\right)^{3} \operatorname{sign}^{3}{\left(x + \left(a^{2} - x^{2}\right)^{2} \right)}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right)^{2} \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|^{2}}}{\left(x + \left(a^{2} - x^{2}\right)^{2}\right) \left|{x + \left(a^{2} - x^{2}\right)^{2}}\right|}$$