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y=x^sin(x)
Derivada de la función/ x^sin/ sin(x)/ y=x^sin(x)

Derivada de y=x^sin(x)

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

Gráfico:

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Solución

Ha introducido [src] 
 sin(x)
x
$$x^{\sin{\left(x \right)}}$$ 
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] 
 sin(x) /sin(x)                \
x      *|------ + cos(x)*log(x)|
        \  x                   /
$$x^{\sin{\left(x \right)}} \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)$$
Simplificar
Segunda derivada [src] 
        /                        2                                    \
 sin(x) |/sin(x)                \    sin(x)                   2*cos(x)|
x      *||------ + cos(x)*log(x)|  - ------ - log(x)*sin(x) + --------|
        |\  x                   /       2                        x    |
        \                              x                              /
$$x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{2} - \log{\left(x \right)} \sin{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{\sin{\left(x \right)}}{x^{2}}\right)$$
Simplificar
3-я производная [src] 
        /                        3                                                                                                                  \
 sin(x) |/sin(x)                \                    3*sin(x)   3*cos(x)     /sin(x)                \ /sin(x)                   2*cos(x)\   2*sin(x)|
x      *||------ + cos(x)*log(x)|  - cos(x)*log(x) - -------- - -------- - 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------| + --------|
        |\  x                   /                       x           2        \  x                   / |   2                        x    |       3   |
        \                                                          x                                  \  x                              /      x    /
$$x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - \log{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}\right)$$
Simplificar
Tercera derivada [src] 
        /                        3                                                                                                                  \
 sin(x) |/sin(x)                \                    3*sin(x)   3*cos(x)     /sin(x)                \ /sin(x)                   2*cos(x)\   2*sin(x)|
x      *||------ + cos(x)*log(x)|  - cos(x)*log(x) - -------- - -------- - 3*|------ + cos(x)*log(x)|*|------ + log(x)*sin(x) - --------| + --------|
        |\  x                   /                       x           2        \  x                   / |   2                        x    |       3   |
        \                                                          x                                  \  x                              /      x    /
$$x^{\sin{\left(x \right)}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right)^{3} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{\sin{\left(x \right)}}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{\sin{\left(x \right)}}{x^{2}}\right) - \log{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2 \sin{\left(x \right)}}{x^{3}}\right)$$
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Gráfico
Derivada de y=x^sin(x)
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