Derivada de x^sin6x

Ha introducido [src]

 sin(6*x)
x

x^{\sin{\left(6 x \right)}}

x^sin(6*x)

Solución detallada

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Perola derivada

$\left(\log{\left(\sin{\left(6 x \right)} \right)} + 1\right) \sin^{\sin{\left(6 x \right)}}{\left(6 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(6 x \right)} \right)} + 1\right) \sin^{\sin{\left(6 x \right)}}{\left(6 x \right)}$

Gráfica

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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)

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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

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Expresiones idénticas

Derivada de x^sin6x

Gráfico:

Definida a trozos:

Solución