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  • (x*(x- tres)^ dos)^(uno / tres)x*exp(-x)
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  • (x multiplicar por (x menos tres) en el grado dos) en el grado (uno dividir por tres)x multiplicar por exponente de ( menos x)
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  • (x(x-3)^2)^(1/3)xexp(-x)
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  • (x*(x-3)^2)^(1/3)x*exp(x)
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Derivada de la función/ (x-3)/ x*exp/ exp(-x)/ (x*(x-3)^2)^(1/3)/ (x*(x-3)^2)^(1/3)x*exp(-x)

Derivada de (x*(x-3)^2)^(1/3)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 - 3)  *x*e
xx(x−3)23e−xx \sqrt[3]{x \left(x - 3\right)^{2}} e^{- x} 
((x*(x - 3)^2)^(1/3)*x)*exp(-x)
Primera derivada [src] 
/                                   /       2               \\                             
|                  3 ___        2/3 |(x - 3)    x*(-6 + 2*x)||                             
|   ____________   \/ x *|x - 3|   *|-------- + ------------||                             
|3 /          2                     \   3            3      /|  -x     3 ___        2/3  -x
|\/  x*(x - 3)   + ------------------------------------------|*e   - x*\/ x *|x - 3|   *e  
|                                          2                 |                             
\                                   (x - 3)                  /
−xx3∣x−3∣23e−x+(x3(x(2x−6)3+(x−3)23)∣x−3∣23(x−3)2+x(x−3)23)e−x- x \sqrt[3]{x} \left|{x - 3}\right|^{\frac{2}{3}} e^{- x} + \left(\frac{\sqrt[3]{x} \left(\frac{x \left(2 x - 6\right)}{3} + \frac{\left(x - 3\right)^{2}}{3}\right) \left|{x - 3}\right|^{\frac{2}{3}}}{\left(x - 3\right)^{2}} + \sqrt[3]{x \left(x - 3\right)^{2}}\right) e^{- x}
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Segunda derivada [src] 
/                     /         /        2/3     3 ___             \                                                                           \                                                            \    
|                     |         ||-3 + x|      2*\/ x *sign(-3 + x)|                                                                           |                                                            |    
|                     |(-1 + x)*|----------- + --------------------|                                                                           |                                                            |    
|                     |         |     2/3          3 __________    |             2/3                      2/3                      2/3         |             2/3                                            |    
|                     |         \    x             \/ |-3 + x|     /   3*|-3 + x|   *(-1 + x)   6*|-3 + x|   *(-1 + x)   6*|-3 + x|   *(-2 + x)|   6*|-3 + x|   *(-1 + x)                                   |    
|                   x*|--------------------------------------------- - ---------------------- - ---------------------- + ----------------------| + ----------------------                                   |    
|                     |                      x                                   5/3                 2/3                      2/3              |             2/3                                            |    
| 4/3         2/3     \                                                         x                   x   *(-3 + x)            x   *(-3 + x)     /            x                 3 ___         2/3 /    -1 + x\|  -x
|x   *|-3 + x|    + ----------------------------------------------------------------------------------------------------------------------------------------------------- - 2*\/ x *|-3 + x|   *|1 + ------||*e  
\                                                                                         3*(-3 + x)                                                                                            \    -3 + x//
(x43∣x−3∣23−2x3(1+x−1x−3)∣x−3∣23+x((x−1)(2x3sign⁡(x−3)∣x−3∣3+∣x−3∣23x23)x+6(x−2)∣x−3∣23x23(x−3)−6(x−1)∣x−3∣23x23(x−3)−3(x−1)∣x−3∣23x53)+6(x−1)∣x−3∣23x233(x−3))e−x\left(x^{\frac{4}{3}} \left|{x - 3}\right|^{\frac{2}{3}} - 2 \sqrt[3]{x} \left(1 + \frac{x - 1}{x - 3}\right) \left|{x - 3}\right|^{\frac{2}{3}} + \frac{x \left(\frac{\left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x} + \frac{6 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{3 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}\right) + \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}}{3 \left(x - 3\right)}\right) e^{- x}
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Tercera derivada [src] 
/                       /         /        2/3     3 ___             \                                                                           \                              /             /        2/3     3 ___             \              /          2/3   3 ___     2                                 3 ___                   \                                                                                                             /        2/3     3 ___             \                                        /        2/3     3 ___             \                                                                                                              \                                        /        2/3     3 ___             \                                                                                       \    
|                       |         ||-3 + x|      2*\/ x *sign(-3 + x)|                                                                           |                              |             ||-3 + x|      2*\/ x *sign(-3 + x)|              |  |-3 + x|      \/ x *sign (-3 + x)     2*sign(-3 + x)    6*\/ x *DiracDelta(-3 + x)|                                                                                                             ||-3 + x|      2*\/ x *sign(-3 + x)|                                        ||-3 + x|      2*\/ x *sign(-3 + x)|                                                                                                              |                                        ||-3 + x|      2*\/ x *sign(-3 + x)|                                                                                       |    
|                       |(-1 + x)*|----------- + --------------------|                                                                           |                              |  3*(-1 + x)*|----------- + --------------------|   2*(-1 + x)*|- ----------- - ------------------- + ----------------- + --------------------------|                                                                                                  6*(-1 + x)*|----------- + --------------------|                             6*(-2 + x)*|----------- + --------------------|                                                                                                              |                             9*(-1 + x)*|----------- + --------------------|                                                                                       |    
|                       |         |     2/3          3 __________    |             2/3                      2/3                      2/3         |             2/3              |             |     2/3          3 __________    |              |       5/3                  4/3        2/3 3 __________          3 __________       |              2/3                       2/3              2/3                       2/3                       |     2/3          3 __________    |                                        |     2/3          3 __________    |              2/3                       2/3                                                                   |              2/3                       |     2/3          3 __________    |              2/3                       2/3                                            |    
|                       |         \    x             \/ |-3 + x|     /   3*|-3 + x|   *(-1 + x)   6*|-3 + x|   *(-1 + x)   6*|-3 + x|   *(-2 + x)|   6*|-3 + x|   *(-1 + x)     |             \    x             \/ |-3 + x|     /              \      x             |-3 + x|          x   *\/ |-3 + x|           \/ |-3 + x|        /   15*|-3 + x|   *(-1 + x)   18*|-3 + x|      72*|-3 + x|   *(-2 + x)   30*|-3 + x|   *(-2 + x)              \    x             \/ |-3 + x|     /   6*(-1 + x)*sign(-3 + x)              \    x             \/ |-3 + x|     /   30*|-3 + x|   *(-1 + x)   54*|-3 + x|   *(-1 + x)    12*(-1 + x)*sign(-3 + x)     12*(-2 + x)*sign(-3 + x) |   27*|-3 + x|   *(-1 + x)              \    x             \/ |-3 + x|     /   54*|-3 + x|   *(-1 + x)   54*|-3 + x|   *(-2 + x)                                   |    
|                     x*|--------------------------------------------- - ---------------------- - ---------------------- + ----------------------| + ----------------------   x*|- ----------------------------------------------- + ------------------------------------------------------------------------------------------------- + ----------------------- + -------------- - ----------------------- - ----------------------- - ----------------------------------------------- - ----------------------- + ----------------------------------------------- + ----------------------- + ----------------------- - -------------------------- + --------------------------| - ----------------------- + ----------------------------------------------- - ----------------------- + -----------------------                                   |    
|                       |                      x                                   5/3                 2/3                      2/3              |             2/3              |                          2                                                                         x                                                              8/3             2/3                   2/3         2             5/3                                    x*(-3 + x)                         5/3 3 __________                         x*(-3 + x)                           5/3                       2/3         2        2/3          3 __________    2/3          3 __________|              5/3                                   x                                2/3                       2/3                                                 |    
|   4/3         2/3     \                                                         x                   x   *(-3 + x)            x   *(-3 + x)     /            x                 \                         x                                                                                                                                        x               x   *(-3 + x)         x   *(-3 + x)             x   *(-3 + x)                                                             x   *\/ |-3 + x|                                                              x   *(-3 + x)             x   *(-3 + x)        x   *(-3 + x)*\/ |-3 + x|    x   *(-3 + x)*\/ |-3 + x| /             x                                                                      x   *(-3 + x)             x   *(-3 + x)          3 ___         2/3 /    -1 + x\|  -x
|- x   *|-3 + x|    - ----------------------------------------------------------------------------------------------------------------------------------------------------- + ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------ + 3*\/ x *|-3 + x|   *|1 + ------||*e  
\                                                                                             -3 + x                                                                                                                                                                                                                                                                                                                                                                                       9*(-3 + x)                                                                                                                                                                                                                                                                                                                                    \    -3 + x//
(−x43∣x−3∣23+3x3(1+x−1x−3)∣x−3∣23−x((x−1)(2x3sign⁡(x−3)∣x−3∣3+∣x−3∣23x23)x+6(x−2)∣x−3∣23x23(x−3)−6(x−1)∣x−3∣23x23(x−3)−3(x−1)∣x−3∣23x53)+6(x−1)∣x−3∣23x23x−3+x(2(x−1)(6x3δ(x−3)∣x−3∣3−x3sign⁡2(x−3)∣x−3∣43+2sign⁡(x−3)x23∣x−3∣3−∣x−3∣23x53)x+6(x−2)(2x3sign⁡(x−3)∣x−3∣3+∣x−3∣23x23)x(x−3)−6(x−1)(2x3sign⁡(x−3)∣x−3∣3+∣x−3∣23x23)x(x−3)−3(x−1)(2x3sign⁡(x−3)∣x−3∣3+∣x−3∣23x23)x2+12(x−2)sign⁡(x−3)x23(x−3)∣x−3∣3−12(x−1)sign⁡(x−3)x23(x−3)∣x−3∣3+18∣x−3∣23x23(x−3)−72(x−2)∣x−3∣23x23(x−3)2+54(x−1)∣x−3∣23x23(x−3)2−6(x−1)sign⁡(x−3)x53∣x−3∣3−30(x−2)∣x−3∣23x53(x−3)+30(x−1)∣x−3∣23x53(x−3)+15(x−1)∣x−3∣23x83)+9(x−1)(2x3sign⁡(x−3)∣x−3∣3+∣x−3∣23x23)x+54(x−2)∣x−3∣23x23(x−3)−54(x−1)∣x−3∣23x23(x−3)−27(x−1)∣x−3∣23x539(x−3))e−x\left(- x^{\frac{4}{3}} \left|{x - 3}\right|^{\frac{2}{3}} + 3 \sqrt[3]{x} \left(1 + \frac{x - 1}{x - 3}\right) \left|{x - 3}\right|^{\frac{2}{3}} - \frac{x \left(\frac{\left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x} + \frac{6 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{3 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}\right) + \frac{6 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}}{x - 3} + \frac{x \left(\frac{2 \left(x - 1\right) \left(\frac{6 \sqrt[3]{x} \delta\left(x - 3\right)}{\sqrt[3]{\left|{x - 3}\right|}} - \frac{\sqrt[3]{x} \operatorname{sign}^{2}{\left(x - 3 \right)}}{\left|{x - 3}\right|^{\frac{4}{3}}} + \frac{2 \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{2}{3}} \sqrt[3]{\left|{x - 3}\right|}} - \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}\right)}{x} + \frac{6 \left(x - 2\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x \left(x - 3\right)} - \frac{6 \left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x \left(x - 3\right)} - \frac{3 \left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x^{2}} + \frac{12 \left(x - 2\right) \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{2}{3}} \left(x - 3\right) \sqrt[3]{\left|{x - 3}\right|}} - \frac{12 \left(x - 1\right) \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{2}{3}} \left(x - 3\right) \sqrt[3]{\left|{x - 3}\right|}} + \frac{18 \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{72 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)^{2}} + \frac{54 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)^{2}} - \frac{6 \left(x - 1\right) \operatorname{sign}{\left(x - 3 \right)}}{x^{\frac{5}{3}} \sqrt[3]{\left|{x - 3}\right|}} - \frac{30 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}} \left(x - 3\right)} + \frac{30 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}} \left(x - 3\right)} + \frac{15 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{8}{3}}}\right) + \frac{9 \left(x - 1\right) \left(\frac{2 \sqrt[3]{x} \operatorname{sign}{\left(x - 3 \right)}}{\sqrt[3]{\left|{x - 3}\right|}} + \frac{\left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}}}\right)}{x} + \frac{54 \left(x - 2\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{54 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{2}{3}} \left(x - 3\right)} - \frac{27 \left(x - 1\right) \left|{x - 3}\right|^{\frac{2}{3}}}{x^{\frac{5}{3}}}}{9 \left(x - 3\right)}\right) e^{- x}
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