Sr Examen

Derivada de x^(-xsinx)

Función f() - derivada -er orden en el punto
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Gráfico:

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Solución

Ha introducido [src]
 -x*sin(x)
x         
$$x^{- x \sin{\left(x \right)}}$$
x^((-x)*sin(x))
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada

  2. Simplificamos:


Respuesta:

Gráfica
Primera derivada [src]
 -x*sin(x)                                        
x         *(-sin(x) + (-sin(x) - x*cos(x))*log(x))
$$x^{- x \sin{\left(x \right)}} \left(\left(- x \cos{\left(x \right)} - \sin{\left(x \right)}\right) \log{\left(x \right)} - \sin{\left(x \right)}\right)$$
Segunda derivada [src]
 -x*sin(x) /                                     2                                            x*cos(x) + sin(x)\
x         *|((x*cos(x) + sin(x))*log(x) + sin(x))  - cos(x) + (-2*cos(x) + x*sin(x))*log(x) - -----------------|
           \                                                                                          x        /
$$x^{- x \sin{\left(x \right)}} \left(\left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)} + \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right)^{2} - \cos{\left(x \right)} - \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}\right)$$
Tercera derivada [src]
 -x*sin(x) /                                       3   x*cos(x) + sin(x)                                  2*(-2*cos(x) + x*sin(x))                                           /x*cos(x) + sin(x)                                         \         \
x         *|- ((x*cos(x) + sin(x))*log(x) + sin(x))  + ----------------- + (3*sin(x) + x*cos(x))*log(x) + ------------------------ + 3*((x*cos(x) + sin(x))*log(x) + sin(x))*|----------------- - (-2*cos(x) + x*sin(x))*log(x) + cos(x)| + sin(x)|
           |                                                    2                                                    x                                                       \        x                                                 /         |
           \                                                   x                                                                                                                                                                                  /
$$x^{- x \sin{\left(x \right)}} \left(\left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \right)} - \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right)^{3} + 3 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right) \left(- \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)} + \cos{\left(x \right)} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}\right) + \sin{\left(x \right)} + \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2}}\right)$$
Gráfico
Derivada de x^(-xsinx)