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x^(x*sin(x))
Derivada de la función/ x*sin/ sin(x)/ x^(x*sin(x))

Derivada de x^(x*sin(x))

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

Gráfico:

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Definida a trozos:

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

Respuesta:

Gráfica
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
 x*sin(x)                                      
x        *((x*cos(x) + sin(x))*log(x) + sin(x))
$$x^{x \sin{\left(x \right)}} \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right)$$
Simplificar
Segunda derivada [src] 
 x*sin(x) /                                     2   x*cos(x) + sin(x)                                         \
x        *|((x*cos(x) + sin(x))*log(x) + sin(x))  + ----------------- - (-2*cos(x) + x*sin(x))*log(x) + cos(x)|
          \                                                 x                                                 /
$$x^{x \sin{\left(x \right)}} \left(- \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)} + \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right)^{2} + \cos{\left(x \right)} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}\right)$$
Simplificar
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))  - 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)||
          |                                                           2                                                    x                                                       \        x                                                 /|
          \                                                          x                                                                                                                                                                         /
$$x^{x \sin{\left(x \right)}} \left(- \left(x \cos{\left(x \right)} + 3 \sin{\left(x \right)}\right) \log{\left(x \right)} + \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right)^{3} + 3 \left(\left(x \cos{\left(x \right)} + \sin{\left(x \right)}\right) \log{\left(x \right)} + \sin{\left(x \right)}\right) \left(- \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right) \log{\left(x \right)} + \cos{\left(x \right)} + \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x}\right) - \sin{\left(x \right)} - \frac{2 \left(x \sin{\left(x \right)} - 2 \cos{\left(x \right)}\right)}{x} - \frac{x \cos{\left(x \right)} + \sin{\left(x \right)}}{x^{2}}\right)$$
Simplificar
Gráfico
Derivada de x^(x*sin(x))
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