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((x*(x+1))*|x-1|)^(1/3)
Derivada de la función/ |x-1|/ (x+1)/ ((x*(x+1))*|x-1|)^(1/3)

Derivada de ((x*(x+1))*|x-1|)^(1/3)

Función f() - derivada -er orden en el punto
v

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
3 ___________________
\/ x*(x + 1)*|x - 1|
x(x+1)∣x−1∣3\sqrt[3]{x \left(x + 1\right) \left|{x - 1}\right|} 
((x*(x + 1))*|x - 1|)^(1/3)
Gráfica
02468-8-6-4-2-101020-10
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
3 ___________ 3 _________ /(1 + 2*x)*|x - 1|   x*(x + 1)*sign(-1 + x)\
\/ x*(x + 1) *\/ |x - 1| *|----------------- + ----------------------|
                          \        3                     3           /
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                          x*(x + 1)*|x - 1|
x(x+1)3∣x−1∣3(x(x+1)sign⁡(x−1)3+(2x+1)∣x−1∣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|}
Simplificar
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)                                 /
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                                                                                                                                                                                              9*x*(1 + x)
x(x+1)3((sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣+3(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)∣x−1∣23−3(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(x+1)∣x−1∣23−3(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)2−3(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x∣x−1∣23)9x(x+1)\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)}
Simplificar
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)                                 /
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x(x+1)3(3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)∣x−1∣+(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(6δ(x−1)∣x−1∣23−2sign⁡2(x−1)∣x−1∣53+2(2x+1)sign⁡(x−1)x(x+1)∣x−1∣23+6∣x−1∣3x(x+1)−3(2x+1)∣x−1∣3x(x+1)2−3(2x+1)∣x−1∣3x2(x+1)+(2x+1)2∣x−1∣3x2(x+1)2)∣x−1∣−6(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)sign⁡(x−1)∣x−1∣53+18(x(x+1)δ(1)(x−1)+2xδ(x−1)+2(x+1)δ(x−1)+(2x+1)δ(x−1)+3sign⁡(x−1))∣x−1∣23−3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(x+1)∣x−1∣+6(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡(x−1)(x+1)∣x−1∣53−18(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)(x+1)∣x−1∣23+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(x+1)2∣x−1∣23−3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡(x−1)(x−1)2−18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3δ(x−1)(x−1)2−3(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡2(x−1)(x−1)2∣x−1∣23−9(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)2+9(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)2(x+1)+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)3−3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x∣x−1∣+6(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡(x−1)x∣x−1∣53−18(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)x∣x−1∣23+3(2x+1)(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)x(x+1)∣x−1∣23+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x(x+1)∣x−1∣23−3(2x+1)(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x(x+1)2∣x−1∣23+9(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)x(x−1)2−3(2x+1)(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)x(x−1)2(x+1)+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x2∣x−1∣23−3(2x+1)(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x2(x+1)∣x−1∣23)27x(x+1)\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)}
Simplificar
3-я производная [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)                                 /
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x(x+1)3(3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)∣x−1∣+(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(6δ(x−1)∣x−1∣23−2sign⁡2(x−1)∣x−1∣53+2(2x+1)sign⁡(x−1)x(x+1)∣x−1∣23+6∣x−1∣3x(x+1)−3(2x+1)∣x−1∣3x(x+1)2−3(2x+1)∣x−1∣3x2(x+1)+(2x+1)2∣x−1∣3x2(x+1)2)∣x−1∣−6(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)sign⁡(x−1)∣x−1∣53+18(x(x+1)δ(1)(x−1)+2xδ(x−1)+2(x+1)δ(x−1)+(2x+1)δ(x−1)+3sign⁡(x−1))∣x−1∣23−3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(x+1)∣x−1∣+6(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡(x−1)(x+1)∣x−1∣53−18(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)(x+1)∣x−1∣23+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)(x+1)2∣x−1∣23−3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡(x−1)(x−1)2−18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3δ(x−1)(x−1)2−3(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡2(x−1)(x−1)2∣x−1∣23−9(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)2+9(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)2(x+1)+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)(x−1)3−3(sign⁡(x−1)∣x−1∣23+(2x+1)∣x−1∣3x(x+1))(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x∣x−1∣+6(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)sign⁡(x−1)x∣x−1∣53−18(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)x∣x−1∣23+3(2x+1)(2x(x+1)δ(x−1)+xsign⁡(x−1)+(x+1)sign⁡(x−1)+(2x+1)sign⁡(x−1)+2∣x−1∣)x(x+1)∣x−1∣23+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x(x+1)∣x−1∣23−3(2x+1)(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x(x+1)2∣x−1∣23+9(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)x(x−1)2−3(2x+1)(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)∣x−1∣3sign⁡(x−1)x(x−1)2(x+1)+18(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x2∣x−1∣23−3(2x+1)(x(x+1)sign⁡(x−1)+(2x+1)∣x−1∣)x2(x+1)∣x−1∣23)27x(x+1)\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)}
Simplificar
Gráfico
Derivada de ((x*(x+1))*|x-1|)^(1/3)
    © Sr Examen – Калькулятор