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(x(x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))
Derivada de la función/ (x(x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))

Derivada de (x(x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   ____________________
3 /                  2 
\/  x*(x - 1)*(x + 2)  
-----------------------
    (x - 1)*(x + 2)
x(x−1)(x+2)23(x−1)(x+2)\frac{\sqrt[3]{x \left(x - 1\right) \left(x + 2\right)^{2}}}{\left(x - 1\right) \left(x + 2\right)} 
((x*(x - 1))*(x + 2)^2)^(1/3)/(((x - 1)*(x + 2)))
Gráfica
02468-8-6-4-2-1010-2525
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
                                                                               /       2                                 \
                                      3 ___________        2/3        1        |(x + 2) *(-1 + 2*x)   x*(4 + 2*x)*(x - 1)|
3 ___________        2/3              \/ x*(x - 1) *|x + 2|   *---------------*|------------------- + -------------------|
\/ x*(x - 1) *|x + 2|   *(-1 - 2*x)                            (x - 1)*(x + 2) \         3                     3         /
----------------------------------- + ------------------------------------------------------------------------------------
                2        2                                                              2                                 
         (x - 1) *(x + 2)                                              x*(x - 1)*(x + 2)
x(x−1)3∣x+2∣23(−2x−1)(x−1)2(x+2)2+x(x−1)31(x−1)(x+2)(x(x−1)(2x+4)3+(x+2)2(2x−1)3)∣x+2∣23x(x−1)(x+2)2\frac{\sqrt[3]{x \left(x - 1\right)} \left|{x + 2}\right|^{\frac{2}{3}} \left(- 2 x - 1\right)}{\left(x - 1\right)^{2} \left(x + 2\right)^{2}} + \frac{\sqrt[3]{x \left(x - 1\right)} \frac{1}{\left(x - 1\right) \left(x + 2\right)} \left(\frac{x \left(x - 1\right) \left(2 x + 4\right)}{3} + \frac{\left(x + 2\right)^{2} \left(2 x - 1\right)}{3}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right) \left(x + 2\right)^{2}}
Simplificar
Segunda derivada [src] 
               /                                                                                                         /                       2/3           \            2/3 /       2                                                                 \            2/3                                                2/3                                                2/3                                                                                                 \
               |                                                                                                         |2*sign(2 + x)   |2 + x|   *(-1 + 2*x)|   6*|2 + x|   *\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   3*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   3*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   6*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))                                                             |
               |                                                                   - ((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|------------- + ---------------------| - ---------------------------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------ + ------------------------------------------------                                                             |
               |                                                                                                         | 3 _________          x*(-1 + x)     |                                            2 + x                                                                    x                                                -1 + x                                             2 + x                                  2/3                                              |
3 ____________ |       2/3 /     1 + 2*x   1 + 2*x             /  1        1  \\                                         \ \/ |2 + x|                          /                                                                                                                                                                                                                                                       2*|2 + x|   *(1 + 2*x)*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))|
\/ x*(-1 + x) *||2 + x|   *|-2 + ------- + ------- + (1 + 2*x)*|------ + -----|| - --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- - ----------------------------------------------------------|
               \           \      -1 + x    2 + x              \-1 + x   2 + x//                                                                                                                                                                  9*x                                                                                                                                                                                     3*x*(-1 + x)*(2 + x)                   /
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                                                                                                                                                                                                                                        2        2                                                                                                                                                                                                                                
                                                                                                                                                                                                                                (-1 + x) *(2 + x)
x(x−1)3(((2x+1)(1x+2+1x−1)−2+2x+1x+2+2x+1x−1)∣x+2∣23−−(2x(x−1)+(x+2)(2x−1))(2sign⁡(x+2)∣x+2∣3+(2x−1)∣x+2∣23x(x−1))+6(2x(x−1)+(x+2)(2x−1))∣x+2∣23x+2−6(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))∣x+2∣23x+2+3(2x(x−1)+(x+2)(2x−1))∣x+2∣23x−1+3(2x(x−1)+(x+2)(2x−1))∣x+2∣23x9x−2(2x+1)(2x(x−1)+(x+2)(2x−1))∣x+2∣233x(x−1)(x+2))(x−1)2(x+2)2\frac{\sqrt[3]{x \left(x - 1\right)} \left(\left(\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right) - 2 + \frac{2 x + 1}{x + 2} + \frac{2 x + 1}{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{- \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)}\right) + \frac{6 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{6 \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x - 1} + \frac{3 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}}{9 x} - \frac{2 \left(2 x + 1\right) \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{3 x \left(x - 1\right) \left(x + 2\right)}\right)}{\left(x - 1\right)^{2} \left(x + 2\right)^{2}}
Simplificar
Tercera derivada [src] 
               /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    /                       2/3           \                                                                                                                     /                       2/3           \                                         /                       2/3           \                                         /                       2/3           \                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 \
               |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    |2*sign(2 + x)   |2 + x|   *(-1 + 2*x)| /       2                                                                 \                                         |2*sign(2 + x)   |2 + x|   *(-1 + 2*x)|                                         |2*sign(2 + x)   |2 + x|   *(-1 + 2*x)|                                         |2*sign(2 + x)   |2 + x|   *(-1 + 2*x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
               |                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                  6*|------------- + ---------------------|*\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   3*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|------------- + ---------------------|   3*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|------------- + ---------------------|   6*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|------------- + ---------------------|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                 |
               |                                                                                                                                                                                                                                         /        2                                          2/3             2        2/3            2/3                       2/3                                      \             2/3                       2/3                                                 2/3                                                 2/3                                         | 3 _________          x*(-1 + x)     |                                                                                                                     | 3 _________          x*(-1 + x)     |                                         | 3 _________          x*(-1 + x)     |                                         | 3 _________          x*(-1 + x)     |             2/3 /       2                                                                 \             2/3                                                 2/3                                                 2/3                                          /       2                                                                 \                                                                                                                                                                                      2/3 /       2                                                                 \             2/3 /       2                                                                 \            2/3                                                           2/3                                                           2/3            /       2                                                                 \            2/3                                                            /                                      /                       2/3           \            2/3 /       2                                                                 \            2/3                                                2/3                                                2/3                                    \                                                                                                       |
               |                                                                                                                                                                                                                                         |  2*sign (2 + x)   12*DiracDelta(2 + x)   6*|2 + x|      (-1 + 2*x) *|2 + x|      3*|2 + x|   *(-1 + 2*x)   3*|2 + x|   *(-1 + 2*x)   4*(-1 + 2*x)*sign(2 + x)|   54*|2 + x|   *(3 + 4*x)   54*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   18*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   18*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))     \ \/ |2 + x|                          /                                                                                                                     \ \/ |2 + x|                          /                                         \ \/ |2 + x|                          /                                         \ \/ |2 + x|                          /   72*|2 + x|   *\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   36*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   36*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   18*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   12*\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/*sign(2 + x)   6*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*sign(2 + x)   6*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*sign(2 + x)   12*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*sign(2 + x)   36*|2 + x|   *\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   36*|2 + x|   *\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   3*|2 + x|   *(-1 + 2*x)*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   3*|2 + x|   *(-1 + 2*x)*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   6*|2 + x|   *(-1 + 2*x)*\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   6*|2 + x|   *(-1 + 2*x)*((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))             |                                      |2*sign(2 + x)   |2 + x|   *(-1 + 2*x)|   6*|2 + x|   *\(2 + x)  + x*(-1 + x) + x*(2 + x) + (-1 + x)*(2 + x) + (-1 + 2*x)*(2 + x)/   3*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   3*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))   6*|2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))|                                                                                                       |
               |             /                                                                                                                 /  1        1  \             /  1        1  \                   \   - ((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|- -------------- + -------------------- + ------------ + ---------------------- - ----------------------- - ----------------------- + ------------------------| - ----------------------- - ------------------------------------------------- - ------------------------------------------------- - ------------------------------------------------- - --------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- - ------------------------------------------------- - ------------------------------------------------- - ------------------------------------------------- - ------------------------------------------------------------------------------------------ + ------------------------------------------------- + ------------------------------------------------- + -------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------- + ----------------------------------------------------------- + ----------------------------------------------------------- - --------------------------------------------------------------------------------------------------- + -----------------------------------------------------------   (1 + 2*x)*|- ((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|------------- + ---------------------| - ---------------------------------------------------------------------------------------- + ------------------------------------------------ + ------------------------------------------------ + ------------------------------------------------|          2/3                                     /     1 + 2*x   1 + 2*x             /  1        1  \\|
               |             |                                                                                                       (1 + 2*x)*|------ + -----|   (1 + 2*x)*|------ + -----|                   |                                         |           4/3         3 _________         x*(-1 + x)          2         2                        2                2                              3 _________ |            2 + x                                        2                                                2                                                      2                                                                               2 + x                                                                                                 x                                                                             -1 + x                                                                          2 + x                                                                                       2                                                               x*(2 + x)                                        (-1 + x)*(2 + x)                                       x*(-1 + x)                                                                 3 _________                                                           3 _________                                             3 _________                                        3 _________                                                           x*(2 + x)                                                                                (-1 + x)*(2 + x)                                                                         2                                                    2                                                                             x*(-1 + x)*(2 + x)                                                                x*(-1 + x)*(2 + x)                                 |                                      | 3 _________          x*(-1 + x)     |                                            2 + x                                                                    x                                                -1 + x                                             2 + x                      |   |2 + x|   *((-1 + 2*x)*(2 + x) + 2*x*(-1 + x))*|-2 + ------- + ------- + (1 + 2*x)*|------ + -----|||
3 ____________ |         2/3 |    8        8                 /    1          1              1        \   3*(1 + 2*x)   3*(1 + 2*x)             \-1 + x   2 + x/             \-1 + x   2 + x/     4*(1 + 2*x)   |                                         \    |2 + x|            \/ |2 + x|                             x *(-1 + x)               x*(-1 + x)                x *(-1 + x)          x*(-1 + x)*\/ |2 + x|  /                                                  (2 + x)                                                x                                               (-1 + x)                                                                                                                                                                                                                                                                                                                                                                                                                                         (2 + x)                                                                                                                                                                                                                                           (2 + x)*\/ |2 + x|                                                          x*\/ |2 + x|                                     (-1 + x)*\/ |2 + x|                                 (2 + x)*\/ |2 + x|                                                                                                                                                                                                                                    x*(-1 + x)                                                    x *(-1 + x)                                                                                                                                                                                                         \                                      \ \/ |2 + x|                          /                                                                                                                                                                                                                                                    /                                                  \      -1 + x    2 + x              \-1 + x   2 + x//|
\/ x*(-1 + x) *|- |2 + x|   *|- ------ - ----- + 2*(1 + 2*x)*|--------- + -------- + ----------------| + ----------- + ----------- + -------------------------- + -------------------------- + ----------------| - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------------------------------------|
               |             |  -1 + x   2 + x               |        2          2   (-1 + x)*(2 + x)|            2             2              -1 + x                       2 + x              (-1 + x)*(2 + x)|                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        27*x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                     3*x*(-1 + x)*(2 + x)                                                                                                                                                                                                        x*(-1 + x)*(2 + x)                                         |
               \             \                               \(-1 + x)    (2 + x)                    /    (-1 + x)       (2 + x)                                                                               /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                        /
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                            2        2                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   
                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (-1 + x) *(2 + x)
x(x−1)3(−(2(2x+1)(1(x+2)2+1(x−1)(x+2)+1(x−1)2)+(2x+1)(1x+2+1x−1)x+2−8x+2+3(2x+1)(x+2)2+(2x+1)(1x+2+1x−1)x−1−8x−1+4(2x+1)(x−1)(x+2)+3(2x+1)(x−1)2)∣x+2∣23−−(2x(x−1)+(x+2)(2x−1))(12δ(x+2)∣x+2∣3−2sign⁡2(x+2)∣x+2∣43+4(2x−1)sign⁡(x+2)x(x−1)∣x+2∣3+6∣x+2∣23x(x−1)−3(2x−1)∣x+2∣23x(x−1)2−3(2x−1)∣x+2∣23x2(x−1)+(2x−1)2∣x+2∣23x2(x−1)2)−54(4x+3)∣x+2∣23x+2+6(2x(x−1)+(x+2)(2x−1))(2sign⁡(x+2)∣x+2∣3+(2x−1)∣x+2∣23x(x−1))x+2+12(2x(x−1)+(x+2)(2x−1))sign⁡(x+2)(x+2)∣x+2∣3−6(2sign⁡(x+2)∣x+2∣3+(2x−1)∣x+2∣23x(x−1))(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))x+2−12(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))sign⁡(x+2)(x+2)∣x+2∣3−54(2x(x−1)+(x+2)(2x−1))∣x+2∣23(x+2)2+72(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))∣x+2∣23(x+2)2+3(2x(x−1)+(x+2)(2x−1))(2sign⁡(x+2)∣x+2∣3+(2x−1)∣x+2∣23x(x−1))x−1+6(2x(x−1)+(x+2)(2x−1))sign⁡(x+2)(x−1)∣x+2∣3−36(2x(x−1)+(x+2)(2x−1))∣x+2∣23(x−1)(x+2)+36(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))∣x+2∣23(x−1)(x+2)−18(2x(x−1)+(x+2)(2x−1))∣x+2∣23(x−1)2+3(2x(x−1)+(x+2)(2x−1))(2sign⁡(x+2)∣x+2∣3+(2x−1)∣x+2∣23x(x−1))x+6(2x(x−1)+(x+2)(2x−1))sign⁡(x+2)x∣x+2∣3−36(2x(x−1)+(x+2)(2x−1))∣x+2∣23x(x+2)+36(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))∣x+2∣23x(x+2)−18(2x(x−1)+(x+2)(2x−1))∣x+2∣23x(x−1)+6(2x−1)(2x(x−1)+(x+2)(2x−1))∣x+2∣23x(x−1)(x+2)−6(2x−1)(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))∣x+2∣23x(x−1)(x+2)+3(2x−1)(2x(x−1)+(x+2)(2x−1))∣x+2∣23x(x−1)2−18(2x(x−1)+(x+2)(2x−1))∣x+2∣23x2+3(2x−1)(2x(x−1)+(x+2)(2x−1))∣x+2∣23x2(x−1)27x+(2x+1)(−(2x(x−1)+(x+2)(2x−1))(2sign⁡(x+2)∣x+2∣3+(2x−1)∣x+2∣23x(x−1))+6(2x(x−1)+(x+2)(2x−1))∣x+2∣23x+2−6(x(x−1)+x(x+2)+(x−1)(x+2)+(x+2)2+(x+2)(2x−1))∣x+2∣23x+2+3(2x(x−1)+(x+2)(2x−1))∣x+2∣23x−1+3(2x(x−1)+(x+2)(2x−1))∣x+2∣23x)3x(x−1)(x+2)+(2x(x−1)+(x+2)(2x−1))((2x+1)(1x+2+1x−1)−2+2x+1x+2+2x+1x−1)∣x+2∣23x(x−1)(x+2))(x−1)2(x+2)2\frac{\sqrt[3]{x \left(x - 1\right)} \left(- \left(2 \left(2 x + 1\right) \left(\frac{1}{\left(x + 2\right)^{2}} + \frac{1}{\left(x - 1\right) \left(x + 2\right)} + \frac{1}{\left(x - 1\right)^{2}}\right) + \frac{\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right)}{x + 2} - \frac{8}{x + 2} + \frac{3 \left(2 x + 1\right)}{\left(x + 2\right)^{2}} + \frac{\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right)}{x - 1} - \frac{8}{x - 1} + \frac{4 \left(2 x + 1\right)}{\left(x - 1\right) \left(x + 2\right)} + \frac{3 \left(2 x + 1\right)}{\left(x - 1\right)^{2}}\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{- \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\frac{12 \delta\left(x + 2\right)}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{2 \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left|{x + 2}\right|^{\frac{4}{3}}} + \frac{4 \left(2 x - 1\right) \operatorname{sign}{\left(x + 2 \right)}}{x \left(x - 1\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{6 \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)} - \frac{3 \left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)^{2}} - \frac{3 \left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{2} \left(x - 1\right)} + \frac{\left(2 x - 1\right)^{2} \left|{x + 2}\right|^{\frac{2}{3}}}{x^{2} \left(x - 1\right)^{2}}\right) - \frac{54 \left(4 x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{6 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)}\right)}{x + 2} + \frac{12 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} - \frac{6 \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)}\right) \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right)}{x + 2} - \frac{12 \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} - \frac{54 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x + 2\right)^{2}} + \frac{72 \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x + 2\right)^{2}} + \frac{3 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)}\right)}{x - 1} + \frac{6 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x - 1\right) \sqrt[3]{\left|{x + 2}\right|}} - \frac{36 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right) \left(x + 2\right)} + \frac{36 \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right) \left(x + 2\right)} - \frac{18 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2}} + \frac{3 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)}\right)}{x} + \frac{6 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \operatorname{sign}{\left(x + 2 \right)}}{x \sqrt[3]{\left|{x + 2}\right|}} - \frac{36 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x + 2\right)} + \frac{36 \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x + 2\right)} - \frac{18 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)} + \frac{6 \left(2 x - 1\right) \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right) \left(x + 2\right)} - \frac{6 \left(2 x - 1\right) \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right) \left(x + 2\right)} + \frac{3 \left(2 x - 1\right) \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)^{2}} - \frac{18 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{2}} + \frac{3 \left(2 x - 1\right) \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{2} \left(x - 1\right)}}{27 x} + \frac{\left(2 x + 1\right) \left(- \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + \frac{\left(2 x - 1\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right)}\right) + \frac{6 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{6 \left(x \left(x - 1\right) + x \left(x + 2\right) + \left(x - 1\right) \left(x + 2\right) + \left(x + 2\right)^{2} + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x - 1} + \frac{3 \left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{3 x \left(x - 1\right) \left(x + 2\right)} + \frac{\left(2 x \left(x - 1\right) + \left(x + 2\right) \left(2 x - 1\right)\right) \left(\left(2 x + 1\right) \left(\frac{1}{x + 2} + \frac{1}{x - 1}\right) - 2 + \frac{2 x + 1}{x + 2} + \frac{2 x + 1}{x - 1}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x - 1\right) \left(x + 2\right)}\right)}{\left(x - 1\right)^{2} \left(x + 2\right)^{2}}
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Gráfico
Derivada de (x(x-1)(x+2)^(2))^(1/3)/((x-1)(x+2))
    © Sr Examen – Калькулятор