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- 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
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- Derivada de:
-
Derivada de e^x*sin(x)
-
Derivada de e^x-e^-x
-
Derivada de √(1-x^2)
-
Derivada de 4*e^(2*x)
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Expresiones idénticas
- y=ln|x+sqrt(x)/(x^ dos -a^ dos)|
- y es igual a ln módulo de x más raíz cuadrada de (x) dividir por (x al cuadrado menos a al cuadrado )|
- y es igual a ln módulo de x más raíz cuadrada de (x) dividir por (x en el grado dos menos a en el grado dos)|
- y=ln|x+√(x)/(x^2-a^2)|
- y=ln|x+sqrt(x)/(x2-a2)|
- y=ln|x+sqrtx/x2-a2|
- y=ln|x+sqrt(x)/(x²-a²)|
- y=ln|x+sqrt(x)/(x en el grado 2-a en el grado 2)|
- y=ln|x+sqrtx/x^2-a^2|
- y=ln|x+sqrt(x) dividir por (x^2-a^2)|
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Expresiones semejantes
- y=ln|x+sqrt(x)/(x^2+a^2)|
- y=ln|x-sqrt(x)/(x^2-a^2)|
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Expresiones con funciones
- ln
- ln(2x)/x
- ln|x|
- ln(x+√(x²+1))
- ln(√x)
- ln(x^2+2x)
- Raíz cuadrada sqrt
- sqrt(x)+1
- sqrt(ln(x))
- sqrt(x)*2^x
- sqrt(5*x)
- sqrt(x^4+2x)
- Módulo |
- |z|*z
- |x|^(π)
- |x|*x*a
- |x*x-5*x|
- |x|*(sin(x))^2
Derivada de y=ln|x+sqrt(x)/(x^2-a^2)|
Solución
Ha introducido
[src]
/| ___ |\ || \/ x || log||x + -------|| || 2 2|| \| x - a |/
$$\log{\left(\left|{\frac{\sqrt{x}}{- a^{2} + x^{2}} + x}\right| \right)}$$
log(Abs(x + sqrt(x)/(x^2 - a^2)))
Primera derivada
[src]
/ / / 1 \ \ / / 1 \ \ \
| | re|---------------| | |im|---------------| | |
|/ / ___ \\ | | ___ / 2 2\| / 3/2 \| | | ___ / 2 2\| / 3/2 \| / ___ \| / ___ \
|| | \/ x || | \\/ x *\x - a // | x || | \\/ x *\x - a // | x || | \/ x || | \/ x |
||x + re|-------||*|1 + ------------------- - 2*re|----------|| + |------------------- - 2*im|----------||*im|-------||*sign|x + -------|
|| | 2 2|| | 2 | 2|| | 2 | 2|| | 2 2|| | 2 2|
|\ \x - a // | |/ 2 2\ || | |/ 2 2\ || \x - a /| \ x - a /
\ \ \\x - a / // \ \\x - a / // /
-----------------------------------------------------------------------------------------------------------------------------------------
/ ___ \ | ___ |
| \/ x | | \/ x |
|x + -------|*|x + -------|
| 2 2| | 2 2|
\ x - a / | x - a |
$$\frac{\left(\left(x + \operatorname{re}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}}\right)}\right) \left(\frac{\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(- a^{2} + x^{2}\right)}\right)}}{2} - 2 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(- a^{2} + x^{2}\right)^{2}}\right)} + 1\right) + \left(\frac{\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(- a^{2} + x^{2}\right)}\right)}}{2} - 2 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(- a^{2} + x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}} + x \right)}}{\left(\frac{\sqrt{x}}{- a^{2} + x^{2}} + x\right) \left|{\frac{\sqrt{x}}{- a^{2} + x^{2}} + x}\right|}$$
Segunda derivada
[src]
2
// / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / 3/2 \ / ___ \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / ___ \
|| | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || | 1 4*x | | \/ x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || 2| \/ x |
||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*|-2 + --------------- + ----------|*sign|-x + -------| ||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *sign |-x + -------|
/ 2 2 \ || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | ___ / 2 2\ 2| | 2 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | 2 2|
|/ / 3/2 \ \ / / 3/2 \ \ / / ___ \ / 5/2 \\ / ___ \ / / ___ \\ / / ___ \ / 5/2 \\| / ___ \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / / ___ \\ |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| | \/ x *\a - x / / 2 2\ | \ a - x / |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| \ a - x /
|| | x | / 1 \| | | x | / 1 \| | / 1 \ | \/ x | | x || | \/ x | | | \/ x || | / 1 \ | \/ x | | x ||| | \/ x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || d | | \/ x || \ \ \\a - x / / / \ \\a - x / / / / \ \a - x / / \ \ \\a - x / / / \ \\a - x / / / /
||4*im|----------| + im|---------------|| + |-2 + 4*re|----------| + re|---------------|| + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||*sign|-x + -------| + 2*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*--|-sign|-x + -------|| + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------
|| | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | | 3/2 / 2 2\| | 2| | 3|| | 2 2| | | 2 2|| | | 3/2 / 2 2\| | 2| | 3||| | 2 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| dx| | 2 2|| ___ / ___ \ | ___ |
|| |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| | \x *\a - x // |/ 2 2\ | |/ 2 2\ || \a - x / \ \a - x // | \x *\a - x // |/ 2 2\ | |/ 2 2\ ||| \ a - x / |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| \ \ a - x // \/ x | \/ x | | \/ x |
\\ \\a - x / / / \ \\a - x / / / \ \\a - x / / \\a - x / // \ \\a - x / / \\a - x / /// \ \ \\a - x / / / \ \\a - x / / / / -x + ------- |-x + -------|*|-x + -------|
2 2 | 2 2| | 2 2|
a - x \ a - x / | a - x |
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___ \ | ___ |
| \/ x | | \/ x |
4*|-x + -------|*|-x + -------|
| 2 2| | 2 2|
\ a - x / | a - x |
$$\frac{2 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right) + \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)} - \frac{\left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{2} \operatorname{sign}^{2}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} + \frac{\left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}}{4 \left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|}$$
Tercera derivada
[src]
/ 2 2 \ 3 2 / 2 2 \ 2 2
// / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / 3/2 \ / / ___ \\ / 3/2 \ |/ / 3/2 \ \ / / 3/2 \ \ / / ___ \ / 5/2 \\ / ___ \ / / ___ \\ / / ___ \ / 5/2 \\| / ___ \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / ___ \ / 3/2 \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / ___ \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / ___ 5/2 \ / ___ \ / ___ \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ |/ / 3/2 \ \ / / 3/2 \ \ / / ___ \ / 5/2 \\ / ___ \ / / ___ \\ / / ___ \ / 5/2 \\| // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / ___ \ / 3/2 \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ / / ___ \\ / ___ \
|| | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || | 1 4*x | d | | \/ x || | 1 4*x | || | x | / 1 \| | | x | / 1 \| | / 1 \ | \/ x | | x || | \/ x | | | \/ x || | / 1 \ | \/ x | | x ||| | \/ x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || 3| \/ x | | 1 4*x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || | \/ x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || | 1 16*\/ x 32*x | | \/ x | 2| \/ x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || || | x | / 1 \| | | x | / 1 \| | / 1 \ | \/ x | | x || | \/ x | | | \/ x || | / 1 \ | \/ x | | x ||| || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || 2| \/ x | | 1 4*x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || d | | \/ x || | \/ x |
4*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*|-2 + --------------- + ----------|*--|-sign|-x + -------|| 2*|-2 + --------------- + ----------|*||4*im|----------| + im|---------------|| + |-2 + 4*re|----------| + re|---------------|| + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||*sign|-x + -------| 2*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *sign |-x + -------| 2*|-2 + --------------- + ----------| *||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*sign|-x + -------| ||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*|- ---- + -------- + ----------|*sign|-x + -------| 3*sign |-x + -------|*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*||4*im|----------| + im|---------------|| + |-2 + 4*re|----------| + re|---------------|| + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------||| 3*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *sign |-x + -------|*|-2 + --------------- + ----------| 6*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------|| *--|-sign|-x + -------||*sign|-x + -------|
/ 2 2 \ || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | ___ / 2 2\ 2| dx| | 2 2|| | ___ / 2 2\ 2| || | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | | 3/2 / 2 2\| | 2| | 3|| | 2 2| | | 2 2|| | | 3/2 / 2 2\| | 2| | 3||| | 2 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | 2 2| | ___ / 2 2\ 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | 2 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | 3/2 2 2 2| | 2 2| | 2 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| || | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | | 3/2 / 2 2\| | 2| | 3|| | 2 2| | | 2 2|| | | 3/2 / 2 2\| | 2| | 3||| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| | 2 2| | ___ / 2 2\ 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| dx| | 2 2|| | 2 2|
|/ / 3/2 \ \ / / 3/2 \ \ / / ___ \ / 5/2 \\ / ___ \ / / ___ \\ / / ___ \ / 5/2 \\| / / ___ \\ // / 3/2 \ \ / / ___ \ / 5/2 \\ / / 3/2 \ \ / / ___ \ / 5/2 \\ / / 3/2 \ / 7/2 \ \ / ___ \ / / ___ \\ / / 3/2 \ / 7/2 \ \\ / ___ \ // / ___ \\ / / 3/2 \ \ / / 3/2 \ \ / ___ \\ 2/ / ___ \\ |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| | \/ x *\a - x / / 2 2\ | \ \ a - x // | \/ x *\a - x / / 2 2\ | || |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| | \x *\a - x // |/ 2 2\ | |/ 2 2\ || \a - x / \ \a - x // | \x *\a - x // |/ 2 2\ | |/ 2 2\ ||| \ a - x / |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| \ a - x / | \/ x *\a - x / / 2 2\ | |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| \ a - x / |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| | x a - x / 2 2\ | \ a - x / \ a - x / |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| || |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| | \x *\a - x // |/ 2 2\ | |/ 2 2\ || \a - x / \ \a - x // | \x *\a - x // |/ 2 2\ | |/ 2 2\ ||| |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| \ a - x / | \/ x *\a - x / / 2 2\ | |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| \ \ a - x // \ a - x /
|| | x | / 1 \| | | x | / 1 \| | / 1 \ | \/ x | | x || | \/ x | | | \/ x || | / 1 \ | \/ x | | x ||| d | | \/ x || || | x | / 1 \| | / 1 \ | \/ x | | x || | | x | / 1 \| | / 1 \ | \/ x | | x || | / 1 \ | x | | x | / 1 \| | \/ x | | | \/ x || | / 1 \ | x | | x | / 1 \|| | \/ x | || | \/ x || | | x | / 1 \| | | x | / 1 \| | \/ x || d | | \/ x || \ \ \\a - x / / / \ \\a - x / / / / \ \a - x / / \ \a - x / / \\ \\a - x / / / \ \\a - x / / / \ \\a - x / / \\a - x / // \ \\a - x / / \\a - x / /// \ \ \\a - x / / / \ \\a - x / / / / \ \a - x / / \ \ \\a - x / / / \ \\a - x / / / / \ \ \\a - x / / / \ \\a - x / / / / \ \a - x / / \ \ \\a - x / / / \ \\a - x / / / / \\ \\a - x / / / \ \\a - x / / / \ \\a - x / / \\a - x / // \ \\a - x / / \\a - x / /// \ \ \\a - x / / / \ \\a - x / / / / \ \a - x / / \ \ \\a - x / / / \ \\a - x / / / /
- 4*||4*im|----------| + im|---------------|| + |-2 + 4*re|----------| + re|---------------|| + |- im|--------------| + 16*im|----------| + 32*im|----------||*im|-------| - |x - re|-------||*|- re|--------------| + 16*re|----------| + 32*re|----------|||*--|-sign|-x + -------|| + 3*||4*im|----------| + im|---------------||*|- im|--------------| + 16*im|----------| + 32*im|----------|| + |-2 + 4*re|----------| + re|---------------||*|- re|--------------| + 16*re|----------| + 32*re|----------|| + |4*im|----------------| + 96*im|----------| + 128*im|----------| + im|--------------||*im|-------| - |x - re|-------||*|4*re|----------------| + 96*re|----------| + 128*re|----------| + re|--------------|||*sign|-x + -------| + 4*||x - re|-------||*|-2 + 4*re|----------| + re|---------------|| - |4*im|----------| + im|---------------||*im|-------||*---|-sign|-x + -------|| - -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------------------------------------------------------------------------
|| | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | | 3/2 / 2 2\| | 2| | 3|| | 2 2| | | 2 2|| | | 3/2 / 2 2\| | 2| | 3||| dx| | 2 2|| || | 2| | ___ / 2 2\|| | | 3/2 / 2 2\| | 2| | 3|| | | 2| | ___ / 2 2\|| | | 3/2 / 2 2\| | 2| | 3|| | | 2| | 3| | 4| | 5/2 / 2 2\|| | 2 2| | | 2 2|| | | 2| | 3| | 4| | 5/2 / 2 2\||| | 2 2| || | 2 2|| | | 2| | ___ / 2 2\|| | | 2| | ___ / 2 2\|| | 2 2|| 2| | 2 2|| ___ ___ 2 2 2 / ___ \ / ___ \ | ___ | 2 / ___ \ | ___ |
|| |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| | \x *\a - x // |/ 2 2\ | |/ 2 2\ || \a - x / \ \a - x // | \x *\a - x // |/ 2 2\ | |/ 2 2\ ||| \ \ a - x // || |/ 2 2\ | \\/ x *\a - x //| | \x *\a - x // |/ 2 2\ | |/ 2 2\ || | |/ 2 2\ | \\/ x *\a - x //| | \x *\a - x // |/ 2 2\ | |/ 2 2\ || | | ___ / 2 2\ | |/ 2 2\ | |/ 2 2\ | \x *\a - x //| \a - x / \ \a - x // | | ___ / 2 2\ | |/ 2 2\ | |/ 2 2\ | \x *\a - x //|| \ a - x / |\ \a - x // | |/ 2 2\ | \\/ x *\a - x //| | |/ 2 2\ | \\/ x *\a - x //| \a - x /| dx \ \ a - x // \/ x \/ x / ___ \ | ___ | / ___ \ / 2 2\ | \/ x | | \/ x | | \/ x | / ___ \ | ___ | | \/ x | | \/ x |
\\ \\a - x / / / \ \\a - x / / / \ \\a - x / / \\a - x / // \ \\a - x / / \\a - x / /// \\ \\a - x / / / \ \\a - x / / \\a - x / // \ \\a - x / / / \ \\a - x / / \\a - x / // \ \\/ x *\a - x / / \\a - x / / \\a - x / / / \ \\/ x *\a - x / / \\a - x / / \\a - x / / // \ \ \\a - x / / / \ \\a - x / / / / -x + ------- -x + ------- | \/ x | | \/ x | | \/ x | \a - x /*|-x + -------| |-x + -------|*|-x + -------| | \/ x | | \/ x | |-x + -------|*|-x + -------|
2 2 2 2 |-x + -------| *|-x + -------| |-x + -------| | 2 2| | 2 2| | 2 2| |-x + -------| *|-x + -------| | 2 2| | 2 2|
a - x a - x | 2 2| | 2 2| | 2 2| \ a - x / \ a - x / | a - x | | 2 2| | 2 2| \ a - x / | a - x |
\ a - x / | a - x | \ a - x / \ a - x / | a - x |
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
/ ___ \ | ___ |
| \/ x | | \/ x |
8*|-x + -------|*|-x + -------|
| 2 2| | 2 2|
\ a - x / | a - x |
$$\frac{4 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \frac{\partial^{2}}{\partial x^{2}} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right) - 4 \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right) + 3 \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{x^{\frac{5}{2}} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)^{2}}\right)} + 96 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)} + 128 \operatorname{re}{\left(\frac{x^{\frac{7}{2}}}{\left(a^{2} - x^{2}\right)^{4}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) + \left(\operatorname{im}{\left(\frac{1}{x^{\frac{5}{2}} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)^{2}}\right)} + 96 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)} + 128 \operatorname{im}{\left(\frac{x^{\frac{7}{2}}}{\left(a^{2} - x^{2}\right)^{4}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)} + \frac{6 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{2} \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)} \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right)}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} - \frac{4 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \frac{\partial}{\partial x} \left(- \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}\right)}{\frac{\sqrt{x}}{a^{2} - x^{2}} - x} + \frac{3 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}^{2}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} - \frac{2 \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \left(- \left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(- \operatorname{re}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{re}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{re}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) + \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right)^{2} + \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right)^{2} + \left(- \operatorname{im}{\left(\frac{1}{x^{\frac{3}{2}} \left(a^{2} - x^{2}\right)}\right)} + 16 \operatorname{im}{\left(\frac{\sqrt{x}}{\left(a^{2} - x^{2}\right)^{2}}\right)} + 32 \operatorname{im}{\left(\frac{x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{3}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\frac{\sqrt{x}}{a^{2} - x^{2}} - x} - \frac{2 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{3} \operatorname{sign}^{3}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)^{2} \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|^{2}} + \frac{3 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right)^{2} \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right) \operatorname{sign}^{2}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)^{2} \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|} - \frac{2 \left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{4 x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}} - 2 + \frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)^{2} \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)^{2}} + \frac{\left(\left(x - \operatorname{re}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\operatorname{re}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{re}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)} - 2\right) - \left(\operatorname{im}{\left(\frac{1}{\sqrt{x} \left(a^{2} - x^{2}\right)}\right)} + 4 \operatorname{im}{\left(\frac{x^{\frac{3}{2}}}{\left(a^{2} - x^{2}\right)^{2}}\right)}\right) \operatorname{im}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}}\right)}\right) \left(\frac{32 x^{\frac{5}{2}}}{\left(a^{2} - x^{2}\right)^{2}} + \frac{16 \sqrt{x}}{a^{2} - x^{2}} - \frac{1}{x^{\frac{3}{2}}}\right) \operatorname{sign}{\left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x \right)}}{\left(a^{2} - x^{2}\right) \left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right)}}{8 \left(\frac{\sqrt{x}}{a^{2} - x^{2}} - x\right) \left|{\frac{\sqrt{x}}{a^{2} - x^{2}} - x}\right|}$$