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

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

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
       x*(x + 1)       
-----------------------
           ____________
        3 /          2 
(x + 3)*\/  x*(x + 2)
x(x+1)x(x+2)23(x+3)\frac{x \left(x + 1\right)}{\sqrt[3]{x \left(x + 2\right)^{2}} \left(x + 3\right)} 
(x*(x + 1))/(((x + 3)*(x*(x + 2)^2)^(1/3)))
Primera derivada [src] 
                                                   /                                       /       2              \\
                                                   |                           2/3         |(x + 2)    x*(4 + 2*x)||
                                                   |     ____________   |x + 2|   *(x + 3)*|-------- + -----------||
                                     3 ___         |  3 /          2                       \   3            3     /|
                                     \/ x *(x + 1)*|- \/  x*(x + 2)   - -------------------------------------------|
                                                   |                                    2/3        2               |
           1                                       \                                   x   *(x + 2)                /
------------------------*(1 + 2*x) + -------------------------------------------------------------------------------
3 ___                2/3                                                  2        4/3                              
\/ x *(x + 3)*|x + 2|                                              (x + 3) *|x + 2|
x3(x+1)(−x(x+2)23−(x+3)(x(2x+4)3+(x+2)23)∣x+2∣23x23(x+2)2)(x+3)2∣x+2∣43+1x3(x+3)∣x+2∣23(2x+1)\frac{\sqrt[3]{x} \left(x + 1\right) \left(- \sqrt[3]{x \left(x + 2\right)^{2}} - \frac{\left(x + 3\right) \left(\frac{x \left(2 x + 4\right)}{3} + \frac{\left(x + 2\right)^{2}}{3}\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x + 2\right)^{2}}\right)}{\left(x + 3\right)^{2} \left|{x + 2}\right|^{\frac{4}{3}}} + \frac{1}{\sqrt[3]{x} \left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}} \left(2 x + 1\right)
Simplificar
Segunda derivada [src] 
                                                                  /                                                                                                                                                                            /                                                                2/3                              2/3                              2/3                  \\
                                                                  |  3 ___   (2 + 3*x)*(3 + x)                                                                 /  3 ___   (2 + 3*x)*(3 + x)\     /  3 ___   (2 + 3*x)*(3 + x)\                 |         2/3             (2 + 3*x)*(3 + x)*sign(2 + x)   |2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(3 + x)*(4 + 3*x)||
                                                                  |3*\/ x  + -----------------                                                               3*|3*\/ x  + -----------------|   2*|3*\/ x  + -----------------|*sign(2 + x)   2*|3*|2 + x|   *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------||
                                                                  |              2/3                                                                           |              2/3          |     |              2/3          |                 |                                  3 _________                         x                             2 + x                            2 + x             ||
                    /  3 ___   (2 + 3*x)*(3 + x)\   3 ___         |             x   *(2 + x)     /  3 ___   (2 + 3*x)*(3 + x)\ /1     3     2*sign(2 + x)\     \             x   *(2 + x)  /     \             x   *(2 + x)  /                 \                                  \/ |2 + x|                                                                                                           /|
        2*(1 + 2*x)*|3*\/ x  + -----------------|   \/ x *(1 + x)*|--------------------------- + |3*\/ x  + -----------------|*|- + ----- + -------------| + ------------------------------- + ------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------|
                    |              2/3          |                 |             x                |              2/3          | \x   3 + x      |2 + x|   /                3 + x                                  |2 + x|                                                                                        2/3                2/3                                                                  |
  2                 \             x   *(2 + x)  /                 \                              \             x   *(2 + x)  /                                                                                                                                                                                 x   *(2 + x)*|2 + x|                                                                     /
----- - ----------------------------------------- + -----------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
3 ___                    2/3                                                                                                                                                                                              9*(3 + x)                                                                                                                                                                      
\/ x                  3*x   *(3 + x)                                                                                                                                                                                                                                                                                                                                                                     
---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
                                                                                                                                                                                                           2/3                                                                                                                                                                                           
                                                                                                                                                                                            (3 + x)*|2 + x|
x3(x+1)((3x3+(x+3)(3x+2)x23(x+2))(2sign⁡(x+2)∣x+2∣+3x+3+1x)+2(3x3+(x+3)(3x+2)x23(x+2))sign⁡(x+2)∣x+2∣+3(3x3+(x+3)(3x+2)x23(x+2))x+3+3x3+(x+3)(3x+2)x23(x+2)x−2((x+3)(3x+2)sign⁡(x+2)∣x+2∣3+3(3x+2)∣x+2∣23−3(x+3)(3x+2)∣x+2∣23x+2+3(x+3)(3x+4)∣x+2∣23x+2−(x+3)(3x+2)∣x+2∣23x)x23(x+2)∣x+2∣23)9(x+3)+2x3−2(3x3+(x+3)(3x+2)x23(x+2))(2x+1)3x23(x+3)(x+3)∣x+2∣23\frac{\frac{\sqrt[3]{x} \left(x + 1\right) \left(\left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) + \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x + 3} + \frac{3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}}{x} - \frac{2 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}\right)}{9 \left(x + 3\right)} + \frac{2}{\sqrt[3]{x}} - \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(2 x + 1\right)}{3 x^{\frac{2}{3}} \left(x + 3\right)}}{\left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}}
Simplificar
Tercera derivada [src] 
                                                  /                                                                                                                                                                                                                                                                                                                                                                                                                                                                                /                                                                2/3                              2/3                              2/3                  \     /            2/3                      2/3                                                 2/3                     2/3                 2                                      2/3                              2/3                                                                       2/3                               2/3                                                                                                    2/3                                                     \                                                                                                                                                                             /                                                                2/3                              2/3                              2/3                  \      /                                                                2/3                              2/3                              2/3                  \                                             /                                                                2/3                              2/3                              2/3                  \\             /                                                                                                                                                                            /                                                                2/3                              2/3                              2/3                  \\
                                                  |                                                                                                                                         /  3 ___   (2 + 3*x)*(3 + x)\      /  3 ___   (2 + 3*x)*(3 + x)\   /  3 ___   (2 + 3*x)*(3 + x)\ /1     3     2*sign(2 + x)\      /  3 ___   (2 + 3*x)*(3 + x)\                       /  3 ___   (2 + 3*x)*(3 + x)\ /1     3     2*sign(2 + x)\      /  3 ___   (2 + 3*x)*(3 + x)\          2        /  3 ___   (2 + 3*x)*(3 + x)\     |         2/3             (2 + 3*x)*(3 + x)*sign(2 + x)   |2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(3 + x)*(4 + 3*x)|     |  27*|2 + x|   *(2 + 3*x)   9*|2 + x|   *(2 + 3*x)   9*(2 + 3*x)*sign(2 + x)   27*|2 + x|   *(3 + x)   27*|2 + x|   *(4 + 3*x)   sign (2 + x)*(2 + 3*x)*(3 + x)   36*|2 + x|   *(3 + x)*(4 + 3*x)   5*|2 + x|   *(2 + 3*x)*(3 + x)   6*(2 + 3*x)*(3 + x)*DiracDelta(2 + x)   27*|2 + x|   *(2 + 3*x)*(3 + x)   12*|2 + x|   *(3 + x)*(4 + 3*x)   12*(2 + 3*x)*(3 + x)*sign(2 + x)   4*(2 + 3*x)*(3 + x)*sign(2 + x)   12*|2 + x|   *(2 + 3*x)*(3 + x)   12*(3 + x)*(4 + 3*x)*sign(2 + x)|     /  3 ___   (2 + 3*x)*(3 + x)\ /1     3     2*sign(2 + x)\                 /  3 ___   (2 + 3*x)*(3 + x)\                  /  3 ___   (2 + 3*x)*(3 + x)\                  |         2/3             (2 + 3*x)*(3 + x)*sign(2 + x)   |2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(3 + x)*(4 + 3*x)|      |         2/3             (2 + 3*x)*(3 + x)*sign(2 + x)   |2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(3 + x)*(4 + 3*x)|                 /1     3     2*sign(2 + x)\ |         2/3             (2 + 3*x)*(3 + x)*sign(2 + x)   |2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(3 + x)*(4 + 3*x)||             |  3 ___   (2 + 3*x)*(3 + x)                                                                 /  3 ___   (2 + 3*x)*(3 + x)\     /  3 ___   (2 + 3*x)*(3 + x)\                 |         2/3             (2 + 3*x)*(3 + x)*sign(2 + x)   |2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(2 + 3*x)*(3 + x)   3*|2 + x|   *(3 + x)*(4 + 3*x)||
                                                  |                                                                                                                                       5*|3*\/ x  + -----------------|   27*|3*\/ x  + -----------------|   |3*\/ x  + -----------------|*|- + ----- + -------------|   12*|3*\/ x  + -----------------|*DiracDelta(2 + x)   3*|3*\/ x  + -----------------|*|- + ----- + -------------|   12*|3*\/ x  + -----------------|   14*sign (2 + x)*|3*\/ x  + -----------------|   6*|3*|2 + x|   *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------|   2*|- ----------------------- - ---------------------- + ----------------------- + --------------------- + ----------------------- - ------------------------------ - ------------------------------- + ------------------------------ + ------------------------------------- + ------------------------------- - ------------------------------- - -------------------------------- - ------------------------------- + ------------------------------- + --------------------------------|   2*|3*\/ x  + -----------------|*|- + ----- + -------------|*sign(2 + x)   8*|3*\/ x  + -----------------|*sign(2 + x)   24*|3*\/ x  + -----------------|*sign(2 + x)   18*|3*|2 + x|   *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------|   12*|3*|2 + x|   *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------|*sign(2 + x)   2*|- + ----- + -------------|*|3*|2 + x|   *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------||             |3*\/ x  + -----------------                                                               3*|3*\/ x  + -----------------|   2*|3*\/ x  + -----------------|*sign(2 + x)   2*|3*|2 + x|   *(2 + 3*x) + ----------------------------- - ---------------------------- - ------------------------------ + ------------------------------||
                                                  |                                /                                                        2                                         \     |              2/3          |      |              2/3          |   |              2/3          | \x   3 + x      |2 + x|   /      |              2/3          |                       |              2/3          | \x   3 + x      |2 + x|   /      |              2/3          |                   |              2/3          |     |                                  3 _________                         x                             2 + x                            2 + x             |     |           2 + x                      x                    3 _________                 2 + x                    2 + x                             4/3                                2                             2                              3 _________                                   2                         x*(2 + x)                            3 _________                     3 _________                       x*(2 + x)                            3 _________       |     |              2/3          | \x   3 + x      |2 + x|   /                 |              2/3          |                  |              2/3          |                  |                                  3 _________                         x                             2 + x                            2 + x             |      |                                  3 _________                         x                             2 + x                            2 + x             |                 \x   3 + x      |2 + x|   / |                                  3 _________                         x                             2 + x                            2 + x             ||             |              2/3                                                                           |              2/3          |     |              2/3          |                 |                                  3 _________                         x                             2 + x                            2 + x             ||
    /  3 ___   (2 + 3*x)*(3 + x)\   3 ___         |  /  3 ___   (2 + 3*x)*(3 + x)\ |2       9       6*DiracDelta(2 + x)       3       5*sign (2 + x)   2*sign(2 + x)    6*sign(2 + x) |     \             x   *(2 + x)  /      \             x   *(2 + x)  /   \             x   *(2 + x)  /                                  \             x   *(2 + x)  /                       \             x   *(2 + x)  /                                  \             x   *(2 + x)  /                   \             x   *(2 + x)  /     \                                  \/ |2 + x|                                                                                                           /     \                                                           \/ |2 + x|                                                                      |2 + x|                            (2 + x)                             x                               \/ |2 + x|                             (2 + x)                                                       (2 + x)*\/ |2 + x|                    x*\/ |2 + x|                                                     (2 + x)*\/ |2 + x|        /     \             x   *(2 + x)  /                                             \             x   *(2 + x)  /                  \             x   *(2 + x)  /                  \                                  \/ |2 + x|                                                                                                           /      \                                  \/ |2 + x|                                                                                                           /                                             \                                  \/ |2 + x|                                                                                                           /|             |             x   *(2 + x)     /  3 ___   (2 + 3*x)*(3 + x)\ /1     3     2*sign(2 + x)\     \             x   *(2 + x)  /     \             x   *(2 + x)  /                 \                                  \/ |2 + x|                                                                                                           /|
  2*|3*\/ x  + -----------------|   \/ x *(1 + x)*|2*|3*\/ x  + -----------------|*|-- + -------- - ------------------- + --------- + -------------- + ------------- + ---------------| + ------------------------------- + -------------------------------- + --------------------------------------------------------- - -------------------------------------------------- + ----------------------------------------------------------- + -------------------------------- + --------------------------------------------- - ----------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------------------------------------------------- + ------------------------------------------- + -------------------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------ - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------ - ---------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------|   (1 + 2*x)*|--------------------------- + |3*\/ x  + -----------------|*|- + ----- + -------------| + ------------------------------- + ------------------------------------------- - -----------------------------------------------------------------------------------------------------------------------------------------------------------|
    |              2/3          |                 |  |              2/3          | | 2          2         |2 + x|         x*(3 + x)             2        x*|2 + x|     (3 + x)*|2 + x||                   2                                    2                                           x                                                    |2 + x|                                                    3 + x                                         x*(3 + x)                                         2                                                                                        5/3                2/3                                                                                                                                                                                                                                                                                                        2/3                2/3                                                                                                                                                                                                                                                                      |2 + x|                                                    x*|2 + x|                                  (3 + x)*|2 + x|                                                                                 2/3                        2/3                                                                                                                                           2/3                5/3                                                                                                                                                             2/3                2/3                                                                                |             |             x                |              2/3          | \x   3 + x      |2 + x|   /                3 + x                                  |2 + x|                                                                                        2/3                2/3                                                                  |
    \             x   *(2 + x)  /                 \  \             x   *(2 + x)  / \x    (3 + x)                                         (2 + x)                                      /                  x                              (3 + x)                                                                                                                                                                                                                                                     (2 + x)                                                                                        x   *(2 + x)*|2 + x|                                                                                                                                                                                                                                                                                                          x   *(2 + x)*|2 + x|                                                                                                                                                                                                                                                                                                                                                                                                                                                                              x   *(2 + x)*(3 + x)*|2 + x|                                                                                                                                             x   *(2 + x)*|2 + x|                                                                                                                                                               x   *(2 + x)*|2 + x|                                                                                   /             \                              \             x   *(2 + x)  /                                                                                                                                                                                 x   *(2 + x)*|2 + x|                                                                     /
- ------------------------------- - ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + -------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------
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                x                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                               3*x                                                                                                                                                                        
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                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                    (3 + x) *|2 + x|
−x3(x+1)(2(3x3+(x+3)(3x+2)x23(x+2))(2sign⁡(x+2)∣x+2∣+3x+3+1x)sign⁡(x+2)∣x+2∣+2(3x3+(x+3)(3x+2)x23(x+2))(−6δ(x+2)∣x+2∣+6sign⁡(x+2)(x+3)∣x+2∣+9(x+3)2+5sign⁡2(x+2)(x+2)2+2sign⁡(x+2)x∣x+2∣+3x(x+3)+2x2)−12(3x3+(x+3)(3x+2)x23(x+2))δ(x+2)∣x+2∣+3(3x3+(x+3)(3x+2)x23(x+2))(2sign⁡(x+2)∣x+2∣+3x+3+1x)x+3+24(3x3+(x+3)(3x+2)x23(x+2))sign⁡(x+2)(x+3)∣x+2∣+27(3x3+(x+3)(3x+2)x23(x+2))(x+3)2+14(3x3+(x+3)(3x+2)x23(x+2))sign⁡2(x+2)(x+2)2+(3x3+(x+3)(3x+2)x23(x+2))(2sign⁡(x+2)∣x+2∣+3x+3+1x)x+8(3x3+(x+3)(3x+2)x23(x+2))sign⁡(x+2)x∣x+2∣+12(3x3+(x+3)(3x+2)x23(x+2))x(x+3)+5(3x3+(x+3)(3x+2)x23(x+2))x2−2(2sign⁡(x+2)∣x+2∣+3x+3+1x)((x+3)(3x+2)sign⁡(x+2)∣x+2∣3+3(3x+2)∣x+2∣23−3(x+3)(3x+2)∣x+2∣23x+2+3(x+3)(3x+4)∣x+2∣23x+2−(x+3)(3x+2)∣x+2∣23x)x23(x+2)∣x+2∣23−12((x+3)(3x+2)sign⁡(x+2)∣x+2∣3+3(3x+2)∣x+2∣23−3(x+3)(3x+2)∣x+2∣23x+2+3(x+3)(3x+4)∣x+2∣23x+2−(x+3)(3x+2)∣x+2∣23x)sign⁡(x+2)x23(x+2)∣x+2∣53+2(6(x+3)(3x+2)δ(x+2)∣x+2∣3−(x+3)(3x+2)sign⁡2(x+2)∣x+2∣43+9(3x+2)sign⁡(x+2)∣x+2∣3−12(x+3)(3x+2)sign⁡(x+2)(x+2)∣x+2∣3+12(x+3)(3x+4)sign⁡(x+2)(x+2)∣x+2∣3+27(x+3)∣x+2∣23x+2−27(3x+2)∣x+2∣23x+2+27(3x+4)∣x+2∣23x+2+27(x+3)(3x+2)∣x+2∣23(x+2)2−36(x+3)(3x+4)∣x+2∣23(x+2)2−4(x+3)(3x+2)sign⁡(x+2)x∣x+2∣3−9(3x+2)∣x+2∣23x+12(x+3)(3x+2)∣x+2∣23x(x+2)−12(x+3)(3x+4)∣x+2∣23x(x+2)+5(x+3)(3x+2)∣x+2∣23x2)x23(x+2)∣x+2∣23−18((x+3)(3x+2)sign⁡(x+2)∣x+2∣3+3(3x+2)∣x+2∣23−3(x+3)(3x+2)∣x+2∣23x+2+3(x+3)(3x+4)∣x+2∣23x+2−(x+3)(3x+2)∣x+2∣23x)x23(x+2)(x+3)∣x+2∣23−6((x+3)(3x+2)sign⁡(x+2)∣x+2∣3+3(3x+2)∣x+2∣23−3(x+3)(3x+2)∣x+2∣23x+2+3(x+3)(3x+4)∣x+2∣23x+2−(x+3)(3x+2)∣x+2∣23x)x53(x+2)∣x+2∣23)27−2(3x3+(x+3)(3x+2)x23(x+2))x23+(2x+1)((3x3+(x+3)(3x+2)x23(x+2))(2sign⁡(x+2)∣x+2∣+3x+3+1x)+2(3x3+(x+3)(3x+2)x23(x+2))sign⁡(x+2)∣x+2∣+3(3x3+(x+3)(3x+2)x23(x+2))x+3+3x3+(x+3)(3x+2)x23(x+2)x−2((x+3)(3x+2)sign⁡(x+2)∣x+2∣3+3(3x+2)∣x+2∣23−3(x+3)(3x+2)∣x+2∣23x+2+3(x+3)(3x+4)∣x+2∣23x+2−(x+3)(3x+2)∣x+2∣23x)x23(x+2)∣x+2∣23)3x23(x+3)2∣x+2∣23\frac{- \frac{\sqrt[3]{x} \left(x + 1\right) \left(\frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + 2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(- \frac{6 \delta\left(x + 2\right)}{\left|{x + 2}\right|} + \frac{6 \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 3\right) \left|{x + 2}\right|} + \frac{9}{\left(x + 3\right)^{2}} + \frac{5 \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left(x + 2\right)^{2}} + \frac{2 \operatorname{sign}{\left(x + 2 \right)}}{x \left|{x + 2}\right|} + \frac{3}{x \left(x + 3\right)} + \frac{2}{x^{2}}\right) - \frac{12 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \delta\left(x + 2\right)}{\left|{x + 2}\right|} + \frac{3 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right)}{x + 3} + \frac{24 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 3\right) \left|{x + 2}\right|} + \frac{27 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{\left(x + 3\right)^{2}} + \frac{14 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left(x + 2\right)^{2}} + \frac{\left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right)}{x} + \frac{8 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{x \left|{x + 2}\right|} + \frac{12 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x \left(x + 3\right)} + \frac{5 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x^{2}} - \frac{2 \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}} - \frac{12 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right) \operatorname{sign}{\left(x + 2 \right)}}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{5}{3}}} + \frac{2 \left(\frac{6 \left(x + 3\right) \left(3 x + 2\right) \delta\left(x + 2\right)}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}^{2}{\left(x + 2 \right)}}{\left|{x + 2}\right|^{\frac{4}{3}}} + \frac{9 \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} - \frac{12 \left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{12 \left(x + 3\right) \left(3 x + 4\right) \operatorname{sign}{\left(x + 2 \right)}}{\left(x + 2\right) \sqrt[3]{\left|{x + 2}\right|}} + \frac{27 \left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{27 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{27 \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{27 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x + 2\right)^{2}} - \frac{36 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{\left(x + 2\right)^{2}} - \frac{4 \left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{x \sqrt[3]{\left|{x + 2}\right|}} - \frac{9 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x} + \frac{12 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x + 2\right)} - \frac{12 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x \left(x + 2\right)} + \frac{5 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x^{2}}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}} - \frac{18 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left(x + 3\right) \left|{x + 2}\right|^{\frac{2}{3}}} - \frac{6 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{5}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}\right)}{27} - \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x^{\frac{2}{3}}} + \frac{\left(2 x + 1\right) \left(\left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \left(\frac{2 \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3}{x + 3} + \frac{1}{x}\right) + \frac{2 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right) \operatorname{sign}{\left(x + 2 \right)}}{\left|{x + 2}\right|} + \frac{3 \left(3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}\right)}{x + 3} + \frac{3 \sqrt[3]{x} + \frac{\left(x + 3\right) \left(3 x + 2\right)}{x^{\frac{2}{3}} \left(x + 2\right)}}{x} - \frac{2 \left(\frac{\left(x + 3\right) \left(3 x + 2\right) \operatorname{sign}{\left(x + 2 \right)}}{\sqrt[3]{\left|{x + 2}\right|}} + 3 \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}} - \frac{3 \left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} + \frac{3 \left(x + 3\right) \left(3 x + 4\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x + 2} - \frac{\left(x + 3\right) \left(3 x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}{x}\right)}{x^{\frac{2}{3}} \left(x + 2\right) \left|{x + 2}\right|^{\frac{2}{3}}}\right)}{3 x^{\frac{2}{3}}}}{\left(x + 3\right)^{2} \left|{x + 2}\right|^{\frac{2}{3}}}
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