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- Derivada de una función implícitamente dada
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- Derivada de:
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Derivada de x^-8
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Derivada de x^2/lnx
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Derivada de √x+2
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Derivada de (t^(2)+1)÷(t^(1÷2)-1)
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Expresiones idénticas
- ((x*(x+ uno))*|x- uno |)^(uno / tres)
- ((x multiplicar por (x más 1)) multiplicar por módulo de x menos 1|) en el grado (1 dividir por 3)
- ((x multiplicar por (x más uno)) multiplicar por módulo de x menos uno |) en el grado (uno dividir por tres)
- ((x*(x+1))*|x-1|)(1/3)
- x*x+1*|x-1|1/3
- ((x(x+1))|x-1|)^(1/3)
- ((x(x+1))|x-1|)(1/3)
- xx+1|x-1|1/3
- xx+1|x-1|^1/3
- ((x*(x+1))*|x-1|)^(1 dividir por 3)
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Expresiones semejantes
- ((x*(x+1))*|x+1|)^(1/3)
- ((x*(x-1))*|x-1|)^(1/3)
Derivada de ((x*(x+1))*|x-1|)^(1/3)
Solución
Ha introducido
[src]
3 ___________________ \/ x*(x + 1)*|x - 1|
$$\sqrt[3]{x \left(x + 1\right) \left|{x - 1}\right|}$$
((x*(x + 1))*|x - 1|)^(1/3)
Primera derivada
[src]
3 ___________ 3 _________ /(1 + 2*x)*|x - 1| x*(x + 1)*sign(-1 + x)\
\/ x*(x + 1) *\/ |x - 1| *|----------------- + ----------------------|
\ 3 3 /
----------------------------------------------------------------------
x*(x + 1)*|x - 1|
$$\frac{\sqrt[3]{x \left(x + 1\right)} \sqrt[3]{\left|{x - 1}\right|} \left(\frac{x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)}}{3} + \frac{\left(2 x + 1\right) \left|{x - 1}\right|}{3}\right)}{x \left(x + 1\right) \left|{x - 1}\right|}$$
Segunda derivada
[src]
/ / 3 __________ \ \
| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |
| |------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) |
| | 2/3 x*(1 + x) | 3 __________ |
3 ___________ |3*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) \|-1 + x| / 3*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x)|
\/ x*(1 + x) *|---------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------- - ----------------------------------------------- - ----------------------------------------------- - -------------------------------------------------------------------------|
| 2/3 |-1 + x| 2/3 2/3 2 |
\ |-1 + x| x*|-1 + x| (1 + x)*|-1 + x| (-1 + x) /
--------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
9*x*(1 + x)
$$\frac{\sqrt[3]{x \left(x + 1\right)} \left(\frac{\left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{\left|{x - 1}\right|} + \frac{3 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{\left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{\left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2}} - \frac{3 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left|{x - 1}\right|^{\frac{2}{3}}}\right)}{9 x \left(x + 1\right)}$$
Tercera derivada
[src]
/ / 2 3 __________ 2 3 __________ 3 __________ 3 __________ \ / 3 __________ \ / 3 __________ \ / 3 __________ \ / 3 __________ \ \
| | 2*sign (-1 + x) 6*DiracDelta(-1 + x) 6*\/ |-1 + x| (1 + 2*x) *\/ |-1 + x| 3*\/ |-1 + x| *(1 + 2*x) 3*\/ |-1 + x| *(1 + 2*x) 2*(1 + 2*x)*sign(-1 + x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |
| ((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*|- --------------- + -------------------- + -------------- + ----------------------- - ------------------------ - ------------------------ + ------------------------| 3*|------------ + ----------------------|*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 3*|------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*|------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*|------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) |
| | 5/3 2/3 x*(1 + x) 2 2 2 2 2/3 | | 2/3 x*(1 + x) | 3 __________ 3 __________ | 2/3 x*(1 + x) | | 2/3 x*(1 + x) | 2 | 2/3 x*(1 + x) | 3 __________ 3 __________ 3 __________ 3 __________ |
3 ___________ |18*(3*sign(-1 + x) + (1 + 2*x)*DiracDelta(-1 + x) + 2*x*DiracDelta(-1 + x) + 2*(1 + x)*DiracDelta(-1 + x) + x*(1 + x)*DiracDelta(-1 + x, 1)) \ |-1 + x| |-1 + x| x *(1 + x) x*(1 + x) x *(1 + x) x*(1 + x)*|-1 + x| / 18*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 18*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 6*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x))*sign(-1 + x) \|-1 + x| / 18*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 18*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 18*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*DiracDelta(-1 + x) 9*\/ |-1 + x| *(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x))*sign(-1 + x) \|-1 + x| / \|-1 + x| / 3*sign (-1 + x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) \|-1 + x| / 6*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 6*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 18*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 18*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 3*(1 + 2*x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*(1 + 2*x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*(1 + 2*x)*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 9*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 9*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 3*\/ |-1 + x| *(1 + 2*x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x)|
\/ x*(1 + x) *|-------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------ - -------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- - ------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ + ------------------------------------------------------------ + ------------------------------------------------ + -------------------------------------------------------------------------- - --------------------------------------------------------- - --------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------- + ------------------------------------------------------------------------- - -----------------------------------------------------------------------------------|
| 2/3 |-1 + x| 2/3 2/3 5/3 |-1 + x| 2 2/3 2 2/3 2 2 x*|-1 + x| (1 + x)*|-1 + x| 2 2/3 2 5/3 5/3 2/3 3 2 2/3 2 2/3 2/3 2 2 2 |
\ |-1 + x| x*|-1 + x| (1 + x)*|-1 + x| |-1 + x| x *|-1 + x| (1 + x) *|-1 + x| (-1 + x) (-1 + x) (-1 + x) *|-1 + x| (-1 + x) x*|-1 + x| (1 + x)*|-1 + x| x*(1 + x)*|-1 + x| (-1 + x) x*(1 + x) *|-1 + x| x *(1 + x)*|-1 + x| x*(1 + x)*|-1 + x| x*(-1 + x) (1 + x)*(-1 + x) x*(1 + x)*(-1 + x) /
----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
27*x*(1 + x)
$$\frac{\sqrt[3]{x \left(x + 1\right)} \left(\frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{\left|{x - 1}\right|} + \frac{\left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \left(\frac{6 \delta\left(x - 1\right)}{\left|{x - 1}\right|^{\frac{2}{3}}} - \frac{2 \operatorname{sign}^{2}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{5}{3}}} + \frac{2 \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)}}{x \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{6 \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)} - \frac{3 \left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)^{2}} - \frac{3 \left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x^{2} \left(x + 1\right)} + \frac{\left(2 x + 1\right)^{2} \sqrt[3]{\left|{x - 1}\right|}}{x^{2} \left(x + 1\right)^{2}}\right)}{\left|{x - 1}\right|} - \frac{6 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{5}{3}}} + \frac{18 \left(x \left(x + 1\right) \delta^{\left( 1 \right)}\left( x - 1 \right) + 2 x \delta\left(x - 1\right) + 2 \left(x + 1\right) \delta\left(x - 1\right) + \left(2 x + 1\right) \delta\left(x - 1\right) + 3 \operatorname{sign}{\left(x - 1 \right)}\right)}{\left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{\left(x + 1\right) \left|{x - 1}\right|} + \frac{6 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{\left(x + 1\right) \left|{x - 1}\right|^{\frac{5}{3}}} - \frac{18 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{\left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{\left(x + 1\right)^{2} \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2}} - \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \delta\left(x - 1\right)}{\left(x - 1\right)^{2}} - \frac{3 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}^{2}{\left(x - 1 \right)}}{\left(x - 1\right)^{2} \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{9 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2}} + \frac{9 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2} \left(x + 1\right)} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{3}} - \frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left|{x - 1}\right|} + \frac{6 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{x \left|{x - 1}\right|^{\frac{5}{3}}} - \frac{18 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{x \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{3 \left(2 x + 1\right) \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{x \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(2 x + 1\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left(x + 1\right)^{2} \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{9 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{x \left(x - 1\right)^{2}} - \frac{3 \left(2 x + 1\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{x \left(x - 1\right)^{2} \left(x + 1\right)} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x^{2} \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(2 x + 1\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x^{2} \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}}\right)}{27 x \left(x + 1\right)}$$
3-я производная
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/ / 2 3 __________ 2 3 __________ 3 __________ 3 __________ \ / 3 __________ \ / 3 __________ \ / 3 __________ \ / 3 __________ \ \
| | 2*sign (-1 + x) 6*DiracDelta(-1 + x) 6*\/ |-1 + x| (1 + 2*x) *\/ |-1 + x| 3*\/ |-1 + x| *(1 + 2*x) 3*\/ |-1 + x| *(1 + 2*x) 2*(1 + 2*x)*sign(-1 + x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |sign(-1 + x) \/ |-1 + x| *(1 + 2*x)| |
| ((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*|- --------------- + -------------------- + -------------- + ----------------------- - ------------------------ - ------------------------ + ------------------------| 3*|------------ + ----------------------|*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 3*|------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*|------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*|------------ + ----------------------|*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) |
| | 5/3 2/3 x*(1 + x) 2 2 2 2 2/3 | | 2/3 x*(1 + x) | 3 __________ 3 __________ | 2/3 x*(1 + x) | | 2/3 x*(1 + x) | 2 | 2/3 x*(1 + x) | 3 __________ 3 __________ 3 __________ 3 __________ |
3 ___________ |18*(3*sign(-1 + x) + (1 + 2*x)*DiracDelta(-1 + x) + 2*x*DiracDelta(-1 + x) + 2*(1 + x)*DiracDelta(-1 + x) + x*(1 + x)*DiracDelta(-1 + x, 1)) \ |-1 + x| |-1 + x| x *(1 + x) x*(1 + x) x *(1 + x) x*(1 + x)*|-1 + x| / 18*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 18*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 6*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x))*sign(-1 + x) \|-1 + x| / 18*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 18*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 18*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*DiracDelta(-1 + x) 9*\/ |-1 + x| *(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x))*sign(-1 + x) \|-1 + x| / \|-1 + x| / 3*sign (-1 + x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) \|-1 + x| / 6*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 6*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 18*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 18*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 3*(1 + 2*x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*(1 + 2*x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x)) 3*(1 + 2*x)*(2*|-1 + x| + x*sign(-1 + x) + (1 + x)*sign(-1 + x) + (1 + 2*x)*sign(-1 + x) + 2*x*(1 + x)*DiracDelta(-1 + x)) 9*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 9*\/ |-1 + x| *((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x) 3*\/ |-1 + x| *(1 + 2*x)*((1 + 2*x)*|-1 + x| + x*(1 + x)*sign(-1 + x))*sign(-1 + x)|
\/ x*(1 + x) *|-------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------ - -------------------------------------------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------ - --------------------------------------------------------------------------------------- - --------------------------------------------------------------------------------------- - ------------------------------------------------------------- - ---------------------------------------------------------------------------------------------------- + ------------------------------------------------------------ + ------------------------------------------------------------ + ------------------------------------------------ + -------------------------------------------------------------------------- - --------------------------------------------------------- - --------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------- + ------------------------------------------------------------------------- - -----------------------------------------------------------------------------------|
| 2/3 |-1 + x| 2/3 2/3 5/3 |-1 + x| 2 2/3 2 2/3 2 2 x*|-1 + x| (1 + x)*|-1 + x| 2 2/3 2 5/3 5/3 2/3 3 2 2/3 2 2/3 2/3 2 2 2 |
\ |-1 + x| x*|-1 + x| (1 + x)*|-1 + x| |-1 + x| x *|-1 + x| (1 + x) *|-1 + x| (-1 + x) (-1 + x) (-1 + x) *|-1 + x| (-1 + x) x*|-1 + x| (1 + x)*|-1 + x| x*(1 + x)*|-1 + x| (-1 + x) x*(1 + x) *|-1 + x| x *(1 + x)*|-1 + x| x*(1 + x)*|-1 + x| x*(-1 + x) (1 + x)*(-1 + x) x*(1 + x)*(-1 + x) /
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27*x*(1 + x)
$$\frac{\sqrt[3]{x \left(x + 1\right)} \left(\frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{\left|{x - 1}\right|} + \frac{\left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \left(\frac{6 \delta\left(x - 1\right)}{\left|{x - 1}\right|^{\frac{2}{3}}} - \frac{2 \operatorname{sign}^{2}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{5}{3}}} + \frac{2 \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)}}{x \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{6 \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)} - \frac{3 \left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)^{2}} - \frac{3 \left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x^{2} \left(x + 1\right)} + \frac{\left(2 x + 1\right)^{2} \sqrt[3]{\left|{x - 1}\right|}}{x^{2} \left(x + 1\right)^{2}}\right)}{\left|{x - 1}\right|} - \frac{6 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{5}{3}}} + \frac{18 \left(x \left(x + 1\right) \delta^{\left( 1 \right)}\left( x - 1 \right) + 2 x \delta\left(x - 1\right) + 2 \left(x + 1\right) \delta\left(x - 1\right) + \left(2 x + 1\right) \delta\left(x - 1\right) + 3 \operatorname{sign}{\left(x - 1 \right)}\right)}{\left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{\left(x + 1\right) \left|{x - 1}\right|} + \frac{6 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{\left(x + 1\right) \left|{x - 1}\right|^{\frac{5}{3}}} - \frac{18 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{\left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{\left(x + 1\right)^{2} \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2}} - \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \delta\left(x - 1\right)}{\left(x - 1\right)^{2}} - \frac{3 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}^{2}{\left(x - 1 \right)}}{\left(x - 1\right)^{2} \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{9 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2}} + \frac{9 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{2} \left(x + 1\right)} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{\left(x - 1\right)^{3}} - \frac{3 \left(\frac{\operatorname{sign}{\left(x - 1 \right)}}{\left|{x - 1}\right|^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \sqrt[3]{\left|{x - 1}\right|}}{x \left(x + 1\right)}\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left|{x - 1}\right|} + \frac{6 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \operatorname{sign}{\left(x - 1 \right)}}{x \left|{x - 1}\right|^{\frac{5}{3}}} - \frac{18 \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{x \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{3 \left(2 x + 1\right) \left(2 x \left(x + 1\right) \delta\left(x - 1\right) + x \operatorname{sign}{\left(x - 1 \right)} + \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + 2 \left|{x - 1}\right|\right)}{x \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(2 x + 1\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x \left(x + 1\right)^{2} \left|{x - 1}\right|^{\frac{2}{3}}} + \frac{9 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{x \left(x - 1\right)^{2}} - \frac{3 \left(2 x + 1\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right) \sqrt[3]{\left|{x - 1}\right|} \operatorname{sign}{\left(x - 1 \right)}}{x \left(x - 1\right)^{2} \left(x + 1\right)} + \frac{18 \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x^{2} \left|{x - 1}\right|^{\frac{2}{3}}} - \frac{3 \left(2 x + 1\right) \left(x \left(x + 1\right) \operatorname{sign}{\left(x - 1 \right)} + \left(2 x + 1\right) \left|{x - 1}\right|\right)}{x^{2} \left(x + 1\right) \left|{x - 1}\right|^{\frac{2}{3}}}\right)}{27 x \left(x + 1\right)}$$
Gráfico