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y=x^3+1^tg3xexp-x
Expresiones semejantes
y=(x^3-1)^tg3x*exp(-x)
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Expresiones con funciones
Exponente exp
exp(x^1/2)
exp(2*x)
exp(y)

Derivada de la función/ x^3+1/ x*exp/ exp(-x)/ y=(x^3+1)^tg3x*exp(-x)

Derivada de y=(x^3+1)^tg3x*exp(-x)

Solución

Ha introducido [src]

        tan(3*x)    
/ 3    \          -x
\x  + 1/        *e

$$\left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} e^{- x}$$

(x^3 + 1)^tan(3*x)*exp(-x)

Solución detallada

Se aplica la regla de la derivada parcial:

$\frac{d}{d x} \frac{f{\left(x \right)}}{g{\left(x \right)}} = \frac{- f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}}{g^{2}{\left(x \right)}}$

$f{\left(x \right)} = \left(x^{3} + 1\right)^{\tan{\left(3 x \right)}}$ y $g{\left(x \right)} = e^{x}$ .

Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
1. No logro encontrar los pasos en la búsqueda de esta derivada.
  
  Perola derivada
  
  $\left(\log{\left(\tan{\left(3 x \right)} \right)} + 1\right) \tan^{\tan{\left(3 x \right)}}{\left(3 x \right)}$
Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
1. Derivado $e^{x}$ es.
Ahora aplicamos la regla de la derivada de una divesión:

$\left(- \left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} e^{x} + \left(\log{\left(\tan{\left(3 x \right)} \right)} + 1\right) e^{x} \tan^{\tan{\left(3 x \right)}}{\left(3 x \right)}\right) e^{- 2 x}$
Simplificamos:

$\left(- \left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} + \left(\log{\left(\tan{\left(3 x \right)} \right)} + 1\right) \tan^{\tan{\left(3 x \right)}}{\left(3 x \right)}\right) e^{- x}$

Respuesta:

$\left(- \left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} + \left(\log{\left(\tan{\left(3 x \right)} \right)} + 1\right) \tan^{\tan{\left(3 x \right)}}{\left(3 x \right)}\right) e^{- x}$

Primera derivada [src]

          tan(3*x)               tan(3*x) /                                   2         \    
  / 3    \          -x   / 3    \         |/         2     \    / 3    \   3*x *tan(3*x)|  -x
- \x  + 1/        *e   + \x  + 1/        *|\3 + 3*tan (3*x)/*log\x  + 1/ + -------------|*e  
                                          |                                     3       |    
                                          \                                    x  + 1   /

$$\left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} \left(\frac{3 x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \left(3 \tan^{2}{\left(3 x \right)} + 3\right) \log{\left(x^{3} + 1 \right)}\right) e^{- x} - \left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} e^{- x}$$

Simplificar

Segunda derivada [src]

                 /                                                 2                                                                                                                                                 \    
        tan(3*x) |      /                               2         \                                       4               2                               2 /       2     \                                          |    
/     3\         |      |/       2     \    /     3\   x *tan(3*x)|      /       2     \    /     3\   9*x *tan(3*x)   6*x *tan(3*x)   6*x*tan(3*x)   18*x *\1 + tan (3*x)/      /       2     \    /     3\         |  -x
\1 + x /        *|1 + 9*|\1 + tan (3*x)/*log\1 + x / + -----------|  - 6*\1 + tan (3*x)/*log\1 + x / - ------------- - ------------- + ------------ + --------------------- + 18*\1 + tan (3*x)/*log\1 + x /*tan(3*x)|*e  
                 |      |                                      3  |                                              2              3              3                   3                                                 |    
                 |      \                                 1 + x   /                                      /     3\          1 + x          1 + x               1 + x                                                  |    
                 \                                                                                       \1 + x /                                                                                                    /

$$\left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} \left(- \frac{9 x^{4} \tan{\left(3 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{18 x^{2} \left(\tan^{2}{\left(3 x \right)} + 1\right)}{x^{3} + 1} - \frac{6 x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \frac{6 x \tan{\left(3 x \right)}}{x^{3} + 1} + 9 \left(\frac{x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{2} + 18 \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(3 x \right)} - 6 \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} + 1\right) e^{- x}$$

Simplificar

Tercera derivada [src]

                 /                                                   2                                                 3                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                                   \    
        tan(3*x) |        /                               2         \       /                               2         \                                                    /                               2         \ /     4                              2 /       2     \                                         \                     2                   4 /       2     \       2 /       2     \       3                                                                         2                4                 /       2     \       6                                                             2 /       2     \         |    
/     3\         |        |/       2     \    /     3\   x *tan(3*x)|       |/       2     \    /     3\   x *tan(3*x)|    6*tan(3*x)     /       2     \    /     3\      |/       2     \    /     3\   x *tan(3*x)| |  3*x *tan(3*x)   2*x*tan(3*x)   6*x *\1 + tan (3*x)/     /       2     \    /     3\         |      /       2     \     /     3\   81*x *\1 + tan (3*x)/   54*x *\1 + tan (3*x)/   54*x *tan(3*x)      /       2     \    /     3\            18*x*tan(3*x)   9*x *tan(3*x)   27*x *tan(3*x)   54*x*\1 + tan (3*x)/   54*x *tan(3*x)          2      /       2     \    /     3\   162*x *\1 + tan (3*x)/*tan(3*x)|  -x
\1 + x /        *|-1 - 27*|\1 + tan (3*x)/*log\1 + x / + -----------|  + 27*|\1 + tan (3*x)/*log\1 + x / + -----------|  + ---------- + 9*\1 + tan (3*x)/*log\1 + x / + 27*|\1 + tan (3*x)/*log\1 + x / + -----------|*|- ------------- + ------------ + -------------------- + 6*\1 + tan (3*x)/*log\1 + x /*tan(3*x)| + 54*\1 + tan (3*x)/ *log\1 + x / - --------------------- - --------------------- - -------------- - 54*\1 + tan (3*x)/*log\1 + x /*tan(3*x) - ------------- + ------------- + -------------- + -------------------- + -------------- + 108*tan (3*x)*\1 + tan (3*x)/*log\1 + x / + -------------------------------|*e  
                 |        |                                      3  |       |                                      3  |           3                                        |                                      3  | |            2             3                  3                                                |                                                   2                      3                    2                                                         3               3                2                  3                    3                                                                    3            |    
                 |        \                                 1 + x   /       \                                 1 + x   /      1 + x                                         \                                 1 + x   / |    /     3\         1 + x              1 + x                                                 |                                           /     3\                  1 + x             /     3\                                                     1 + x           1 + x         /     3\              1 + x             /     3\                                                                1 + x             |    
                 \                                                                                                                                                                                                     \    \1 + x /                                                                                  /                                           \1 + x /                                    \1 + x /                                                                                   \1 + x /                                \1 + x /                                                                                  /

$$\left(x^{3} + 1\right)^{\tan{\left(3 x \right)}} \left(\frac{54 x^{6} \tan{\left(3 x \right)}}{\left(x^{3} + 1\right)^{3}} - \frac{81 x^{4} \left(\tan^{2}{\left(3 x \right)} + 1\right)}{\left(x^{3} + 1\right)^{2}} + \frac{27 x^{4} \tan{\left(3 x \right)}}{\left(x^{3} + 1\right)^{2}} - \frac{54 x^{3} \tan{\left(3 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{162 x^{2} \left(\tan^{2}{\left(3 x \right)} + 1\right) \tan{\left(3 x \right)}}{x^{3} + 1} - \frac{54 x^{2} \left(\tan^{2}{\left(3 x \right)} + 1\right)}{x^{3} + 1} + \frac{9 x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \frac{54 x \left(\tan^{2}{\left(3 x \right)} + 1\right)}{x^{3} + 1} - \frac{18 x \tan{\left(3 x \right)}}{x^{3} + 1} + 27 \left(\frac{x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{3} - 27 \left(\frac{x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right)^{2} + 27 \left(\frac{x^{2} \tan{\left(3 x \right)}}{x^{3} + 1} + \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)}\right) \left(- \frac{3 x^{4} \tan{\left(3 x \right)}}{\left(x^{3} + 1\right)^{2}} + \frac{6 x^{2} \left(\tan^{2}{\left(3 x \right)} + 1\right)}{x^{3} + 1} + \frac{2 x \tan{\left(3 x \right)}}{x^{3} + 1} + 6 \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(3 x \right)}\right) + 54 \left(\tan^{2}{\left(3 x \right)} + 1\right)^{2} \log{\left(x^{3} + 1 \right)} + 108 \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan^{2}{\left(3 x \right)} - 54 \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} \tan{\left(3 x \right)} + 9 \left(\tan^{2}{\left(3 x \right)} + 1\right) \log{\left(x^{3} + 1 \right)} - 1 + \frac{6 \tan{\left(3 x \right)}}{x^{3} + 1}\right) e^{- x}$$

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Derivada de y=(x^3+1)^tg3x*exp(-x)

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