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Derivada de la función/ (x-1)/ x*exp/ exp(-x)/ ∛(〖x(x-1)〗^2)x*exp(-x)

Derivada de ∛(〖x(x-1)〗^2)x*exp(-x)

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src] 
   ______________      
3 /            2     -x
\/  (x*(x - 1))  *x*e
x(x(x−1))23e−xx \sqrt[3]{\left(x \left(x - 1\right)\right)^{2}} e^{- x} 
(((x*(x - 1))^2)^(1/3)*x)*exp(-x)
Primera derivada [src] 
/   ______________              2/3           \                           
|3 /            2    |x*(x - 1)|   *(-2 + 4*x)|  -x                2/3  -x
|\/  (x*(x - 1))   + -------------------------|*e   - x*|x*(x - 1)|   *e  
\                            3*(x - 1)        /
−xe−x∣x(x−1)∣23+((x(x−1))23+(4x−2)∣x(x−1)∣233(x−1))e−x- x e^{- x} \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}} + \left(\sqrt[3]{\left(x \left(x - 1\right)\right)^{2}} + \frac{\left(4 x - 2\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{3 \left(x - 1\right)}\right) e^{- x}
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Segunda derivada [src] 
/                                             /                                  2/3                          2                                  2/3           \                               \    
|                                             |              2/3   3*|x*(-1 + x)|   *(-1 + 2*x)   2*(-1 + 2*x) *sign(x*(-1 + x))   3*|x*(-1 + x)|   *(-1 + 2*x)|                               |    
|                                           2*|6*|x*(-1 + x)|    - ---------------------------- + ------------------------------ + ----------------------------|                               |    
|                                             |                               -1 + x                     3 ______________                       x              |                 2/3           |    
|              2/3        2/3         2/3     \                                                          \/ |x*(-1 + x)|                                       /   4*|x*(-1 + x)|   *(-1 + 2*x)|  -x
|x*|x*(-1 + x)|    - 2*|x|   *|-1 + x|    + -------------------------------------------------------------------------------------------------------------------- - ----------------------------|*e  
\                                                                                                9*(-1 + x)                                                                 3*(-1 + x)         /
(x∣x(x−1)∣23−2∣x∣23∣x−1∣23−4(2x−1)∣x(x−1)∣233(x−1)+2(2(2x−1)2sign⁡(x(x−1))∣x(x−1)∣3+6∣x(x−1)∣23−3(2x−1)∣x(x−1)∣23x−1+3(2x−1)∣x(x−1)∣23x)9(x−1))e−x\left(x \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}} - 2 \left|{x}\right|^{\frac{2}{3}} \left|{x - 1}\right|^{\frac{2}{3}} - \frac{4 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{3 \left(x - 1\right)} + \frac{2 \left(\frac{2 \left(2 x - 1\right)^{2} \operatorname{sign}{\left(x \left(x - 1\right) \right)}}{\sqrt[3]{\left|{x \left(x - 1\right)}\right|}} + 6 \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}} - \frac{3 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x - 1} + \frac{3 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x}\right)}{9 \left(x - 1\right)}\right) e^{- x}
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Tercera derivada [src] 
/                                                                                                                                                                      /                                              /                                  2/3                            2/3                          2                 \                                                                                                                                                                                                                                                                               \                               \    
|                                                                                                                                                                      |                                              |              2/3   3*|x*(-1 + x)|   *(-1 + 2*x)   3*|x*(-1 + x)|   *(-1 + 2*x)   2*(-1 + 2*x) *sign(x*(-1 + x))|                                                                                                                                                                                                                                                                               |                               |    
|                                                                                                                                                                      |                                            9*|6*|x*(-1 + x)|    - ---------------------------- - ---------------------------- + ------------------------------|                                                                                                                                                                                                                                                                               |                               |    
|                                               /                                  2/3                          2                                  2/3           \     |                 2/3                  2/3     |                                 x                            -1 + x                     3 ______________       |               3     2                            3                                         2/3                             2/3                                                            2                                 2                                   2/3           |                               |    
|                                               |              2/3   3*|x*(-1 + x)|   *(-1 + 2*x)   2*(-1 + 2*x) *sign(x*(-1 + x))   3*|x*(-1 + x)|   *(-1 + 2*x)|     |  36*|x*(-1 + x)|      36*|x*(-1 + x)|        \                                                                                         \/ |x*(-1 + x)|        /   2*(-1 + 2*x) *sign (x*(-1 + x))   12*(-1 + 2*x) *DiracDelta(x*(-1 + x))   18*|x*(-1 + x)|   *(-1 + 2*x)   18*|x*(-1 + x)|   *(-1 + 2*x)   36*(-1 + 2*x)*sign(x*(-1 + x))   12*(-1 + 2*x) *sign(x*(-1 + x))   12*(-1 + 2*x) *sign(x*(-1 + x))   18*|x*(-1 + x)|   *(-1 + 2*x)|                               |    
|                                             2*|6*|x*(-1 + x)|    - ---------------------------- + ------------------------------ + ----------------------------|   2*|- ------------------ - ------------------ + -------------------------------------------------------------------------------------------------------------------- - ------------------------------- + ------------------------------------- + ----------------------------- + ----------------------------- + ------------------------------ - ------------------------------- - ------------------------------- + -----------------------------|                               |    
|                                               |                               -1 + x                     3 ______________                       x              |     |          x                  -1 + x                                                                  x                                                                                 4/3                      3 ______________                            2                                  2                    3 ______________                   3 ______________                     3 ______________                x*(-1 + x)         |                 2/3           |    
|                2/3        2/3         2/3     \                                                          \/ |x*(-1 + x)|                                       /     \                                                                                                                                                                           |x*(-1 + x)|                         \/ |x*(-1 + x)|                            x                           (-1 + x)                     \/ |x*(-1 + x)|                  x*\/ |x*(-1 + x)|             (-1 + x)*\/ |x*(-1 + x)|                                    /   2*|x*(-1 + x)|   *(-1 + 2*x)|  -x
|- x*|x*(-1 + x)|    + 3*|x|   *|-1 + x|    - -------------------------------------------------------------------------------------------------------------------- + --------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------- + ----------------------------|*e  
\                                                                                                  3*(-1 + x)                                                                                                                                                                                                                                                                            27*(-1 + x)                                                                                                                                                                                                                                  -1 + x           /
(−x∣x(x−1)∣23+3∣x∣23∣x−1∣23+2(2x−1)∣x(x−1)∣23x−1−2(2(2x−1)2sign⁡(x(x−1))∣x(x−1)∣3+6∣x(x−1)∣23−3(2x−1)∣x(x−1)∣23x−1+3(2x−1)∣x(x−1)∣23x)3(x−1)+2(12(2x−1)3δ(x(x−1))∣x(x−1)∣3−2(2x−1)3sign⁡2(x(x−1))∣x(x−1)∣43+36(2x−1)sign⁡(x(x−1))∣x(x−1)∣3−12(2x−1)2sign⁡(x(x−1))(x−1)∣x(x−1)∣3−36∣x(x−1)∣23x−1+18(2x−1)∣x(x−1)∣23(x−1)2−12(2x−1)2sign⁡(x(x−1))x∣x(x−1)∣3+9(2(2x−1)2sign⁡(x(x−1))∣x(x−1)∣3+6∣x(x−1)∣23−3(2x−1)∣x(x−1)∣23x−1−3(2x−1)∣x(x−1)∣23x)x−36∣x(x−1)∣23x+18(2x−1)∣x(x−1)∣23x(x−1)+18(2x−1)∣x(x−1)∣23x2)27(x−1))e−x\left(- x \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}} + 3 \left|{x}\right|^{\frac{2}{3}} \left|{x - 1}\right|^{\frac{2}{3}} + \frac{2 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x - 1} - \frac{2 \left(\frac{2 \left(2 x - 1\right)^{2} \operatorname{sign}{\left(x \left(x - 1\right) \right)}}{\sqrt[3]{\left|{x \left(x - 1\right)}\right|}} + 6 \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}} - \frac{3 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x - 1} + \frac{3 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x}\right)}{3 \left(x - 1\right)} + \frac{2 \left(\frac{12 \left(2 x - 1\right)^{3} \delta\left(x \left(x - 1\right)\right)}{\sqrt[3]{\left|{x \left(x - 1\right)}\right|}} - \frac{2 \left(2 x - 1\right)^{3} \operatorname{sign}^{2}{\left(x \left(x - 1\right) \right)}}{\left|{x \left(x - 1\right)}\right|^{\frac{4}{3}}} + \frac{36 \left(2 x - 1\right) \operatorname{sign}{\left(x \left(x - 1\right) \right)}}{\sqrt[3]{\left|{x \left(x - 1\right)}\right|}} - \frac{12 \left(2 x - 1\right)^{2} \operatorname{sign}{\left(x \left(x - 1\right) \right)}}{\left(x - 1\right) \sqrt[3]{\left|{x \left(x - 1\right)}\right|}} - \frac{36 \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x - 1} + \frac{18 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{\left(x - 1\right)^{2}} - \frac{12 \left(2 x - 1\right)^{2} \operatorname{sign}{\left(x \left(x - 1\right) \right)}}{x \sqrt[3]{\left|{x \left(x - 1\right)}\right|}} + \frac{9 \left(\frac{2 \left(2 x - 1\right)^{2} \operatorname{sign}{\left(x \left(x - 1\right) \right)}}{\sqrt[3]{\left|{x \left(x - 1\right)}\right|}} + 6 \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}} - \frac{3 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x - 1} - \frac{3 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x}\right)}{x} - \frac{36 \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x} + \frac{18 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x \left(x - 1\right)} + \frac{18 \left(2 x - 1\right) \left|{x \left(x - 1\right)}\right|^{\frac{2}{3}}}{x^{2}}\right)}{27 \left(x - 1\right)}\right) e^{- x}
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