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Derivada de:
Derivada de 1/(x+3)
Derivada de 4*y
Derivada de (2x-7)^8
Derivada de (-1)/x-3*x
Expresiones idénticas
x^(-tg(x))x*exp(-x)
x en el grado ( menos tg(x))x multiplicar por exponente de ( menos x)
x(-tg(x))x*exp(-x)
x-tgxx*exp-x
x^(-tg(x))xexp(-x)
x(-tg(x))xexp(-x)
x-tgxxexp-x
x^-tgxxexp-x
Expresiones semejantes
x^(-tg(x))x*exp(x)
x^(tg(x))x*exp(-x)

Derivada de la función/ tg(x)/ x*exp/ exp(-x)/ x^(-tg(x))x*exp(-x)

Derivada de x^(-tg(x))x*exp(-x)

Solución

Ha introducido [src]

 -tan(x)    -x
x       *x*e

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

(x^(-tan(x))*x)*exp(-x)

Solución detallada

Se aplica la regla de la derivada parcial:

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

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

Para calcular $\frac{d}{d x} f{\left(x \right)}$ :
1. Según el principio, aplicamos: $x$ tenemos $1$
Para calcular $\frac{d}{d x} g{\left(x \right)}$ :
1. Se aplica la regla de la derivada de una multiplicación:
  
  $\frac{d}{d x} f{\left(x \right)} g{\left(x \right)} = f{\left(x \right)} \frac{d}{d x} g{\left(x \right)} + g{\left(x \right)} \frac{d}{d x} f{\left(x \right)}$
  
  $f{\left(x \right)} = x^{\tan{\left(x \right)}}$ ; calculamos $\frac{d}{d x} f{\left(x \right)}$ :
  1. No logro encontrar los pasos en la búsqueda de esta derivada.
    
    Perola derivada
    
    $\left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$
  $g{\left(x \right)} = e^{x}$ ; calculamos $\frac{d}{d x} g{\left(x \right)}$ :
  1. Derivado $e^{x}$ es.
  Como resultado de: $x^{\tan{\left(x \right)}} e^{x} + \left(\log{\left(\tan{\left(x \right)} \right)} + 1\right) e^{x} \tan^{\tan{\left(x \right)}}{\left(x \right)}$
Ahora aplicamos la regla de la derivada de una divesión:

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

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

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Expresiones semejantes

Derivada de x^(-tg(x))x*exp(-x)

Gráfico:

Definida a trozos:

Solución