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x^sin6x
Derivada de la función/ x^sin/ sin6x/ x^sin6x

Derivada de x^sin6x

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

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Solución

Ha introducido [src] 
 sin(6*x)
x
$$x^{\sin{\left(6 x \right)}}$$ 
x^sin(6*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(6*x) /sin(6*x)                    \
x        *|-------- + 6*cos(6*x)*log(x)|
          \   x                        /
$$x^{\sin{\left(6 x \right)}} \left(6 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{\sin{\left(6 x \right)}}{x}\right)$$
Simplificar
Segunda derivada [src] 
          /                              2                                              \
 sin(6*x) |/sin(6*x)                    \    sin(6*x)                        12*cos(6*x)|
x        *||-------- + 6*cos(6*x)*log(x)|  - -------- - 36*log(x)*sin(6*x) + -----------|
          |\   x                        /        2                                x     |
          \                                     x                                       /
$$x^{\sin{\left(6 x \right)}} \left(\left(6 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{\sin{\left(6 x \right)}}{x}\right)^{2} - 36 \log{\left(x \right)} \sin{\left(6 x \right)} + \frac{12 \cos{\left(6 x \right)}}{x} - \frac{\sin{\left(6 x \right)}}{x^{2}}\right)$$
Simplificar
Tercera derivada [src] 
          /                              3                                                                                                                                                 \
 sin(6*x) |/sin(6*x)                    \                          108*sin(6*x)   18*cos(6*x)     /sin(6*x)                    \ /sin(6*x)   12*cos(6*x)                     \   2*sin(6*x)|
x        *||-------- + 6*cos(6*x)*log(x)|  - 216*cos(6*x)*log(x) - ------------ - ----------- - 3*|-------- + 6*cos(6*x)*log(x)|*|-------- - ----------- + 36*log(x)*sin(6*x)| + ----------|
          |\   x                        /                               x               2         \   x                        / |    2           x                          |        3    |
          \                                                                            x                                         \   x                                       /       x     /
$$x^{\sin{\left(6 x \right)}} \left(\left(6 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{\sin{\left(6 x \right)}}{x}\right)^{3} - 3 \left(6 \log{\left(x \right)} \cos{\left(6 x \right)} + \frac{\sin{\left(6 x \right)}}{x}\right) \left(36 \log{\left(x \right)} \sin{\left(6 x \right)} - \frac{12 \cos{\left(6 x \right)}}{x} + \frac{\sin{\left(6 x \right)}}{x^{2}}\right) - 216 \log{\left(x \right)} \cos{\left(6 x \right)} - \frac{108 \sin{\left(6 x \right)}}{x} - \frac{18 \cos{\left(6 x \right)}}{x^{2}} + \frac{2 \sin{\left(6 x \right)}}{x^{3}}\right)$$
Simplificar
Gráfico
Derivada de x^sin6x
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