Derivada de x^sin3x

Ha introducido [src]

 sin(3*x)
x

x^{\sin{\left(3 x \right)}}

x^sin(3*x)

Solución detallada

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Perola derivada

$\left(\log{\left(\sin{\left(3 x \right)} \right)} + 1\right) \sin^{\sin{\left(3 x \right)}}{\left(3 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(3 x \right)} \right)} + 1\right) \sin^{\sin{\left(3 x \right)}}{\left(3 x \right)}$

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

 sin(3*x) /sin(3*x)                    \
x        *|-------- + 3*cos(3*x)*log(x)|
          \   x                        /

x^{\sin{\left(3 x \right)}} \left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)

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Segunda derivada [src]

          /                              2                                            \
 sin(3*x) |/sin(3*x)                    \    sin(3*x)                       6*cos(3*x)|
x        *||-------- + 3*cos(3*x)*log(x)|  - -------- - 9*log(x)*sin(3*x) + ----------|
          |\   x                        /        2                              x     |
          \                                     x                                     /

x^{\sin{\left(3 x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)^{2} - 9 \log{\left(x \right)} \sin{\left(3 x \right)} + \frac{6 \cos{\left(3 x \right)}}{x} - \frac{\sin{\left(3 x \right)}}{x^{2}}\right)

Simplificar

Tercera derivada [src]

          /                              3                                                                                                                                            \
 sin(3*x) |/sin(3*x)                    \    27*sin(3*x)                        9*cos(3*x)     /sin(3*x)                    \ /sin(3*x)   6*cos(3*x)                    \   2*sin(3*x)|
x        *||-------- + 3*cos(3*x)*log(x)|  - ----------- - 27*cos(3*x)*log(x) - ---------- - 3*|-------- + 3*cos(3*x)*log(x)|*|-------- - ---------- + 9*log(x)*sin(3*x)| + ----------|
          |\   x                        /         x                                  2         \   x                        / |    2          x                         |        3    |
          \                                                                         x                                         \   x                                     /       x     /

x^{\sin{\left(3 x \right)}} \left(\left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)^{3} - 3 \left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right) \left(9 \log{\left(x \right)} \sin{\left(3 x \right)} - \frac{6 \cos{\left(3 x \right)}}{x} + \frac{\sin{\left(3 x \right)}}{x^{2}}\right) - 27 \log{\left(x \right)} \cos{\left(3 x \right)} - \frac{27 \sin{\left(3 x \right)}}{x} - \frac{9 \cos{\left(3 x \right)}}{x^{2}} + \frac{2 \sin{\left(3 x \right)}}{x^{3}}\right)

Simplificar

Gráfico

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Expresiones idénticas

Derivada de x^sin3x

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Solución