Derivada de y=x^(sin2x)

Ha introducido [src]

 sin(2*x)
x

$$x^{\sin{\left(2 x \right)}}$$

x^sin(2*x)

Solución detallada

No logro encontrar los pasos en la búsqueda de esta derivada.

Perola derivada

$\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}$

Respuesta:

$\left(\log{\left(\sin{\left(2 x \right)} \right)} + 1\right) \sin^{\sin{\left(2 x \right)}}{\left(2 x \right)}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

$$x^{\sin{\left(2 x \right)}} \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)$$

Simplificar

Segunda derivada [src]

          /                              2                                            \
 sin(2*x) |/sin(2*x)                    \    sin(2*x)                       4*cos(2*x)|
x        *||-------- + 2*cos(2*x)*log(x)|  - -------- - 4*log(x)*sin(2*x) + ----------|
          |\   x                        /        2                              x     |
          \                                     x                                     /

$$x^{\sin{\left(2 x \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)^{2} - 4 \log{\left(x \right)} \sin{\left(2 x \right)} + \frac{4 \cos{\left(2 x \right)}}{x} - \frac{\sin{\left(2 x \right)}}{x^{2}}\right)$$

Simplificar

Tercera derivada [src]

          /                              3                                                                                                                                           \
 sin(2*x) |/sin(2*x)                    \    12*sin(2*x)                       6*cos(2*x)     /sin(2*x)                    \ /sin(2*x)   4*cos(2*x)                    \   2*sin(2*x)|
x        *||-------- + 2*cos(2*x)*log(x)|  - ----------- - 8*cos(2*x)*log(x) - ---------- - 3*|-------- + 2*cos(2*x)*log(x)|*|-------- - ---------- + 4*log(x)*sin(2*x)| + ----------|
          |\   x                        /         x                                 2         \   x                        / |    2          x                         |        3    |
          \                                                                        x                                         \   x                                     /       x     /

$$x^{\sin{\left(2 x \right)}} \left(\left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right)^{3} - 3 \left(2 \log{\left(x \right)} \cos{\left(2 x \right)} + \frac{\sin{\left(2 x \right)}}{x}\right) \left(4 \log{\left(x \right)} \sin{\left(2 x \right)} - \frac{4 \cos{\left(2 x \right)}}{x} + \frac{\sin{\left(2 x \right)}}{x^{2}}\right) - 8 \log{\left(x \right)} \cos{\left(2 x \right)} - \frac{12 \sin{\left(2 x \right)}}{x} - \frac{6 \cos{\left(2 x \right)}}{x^{2}} + \frac{2 \sin{\left(2 x \right)}}{x^{3}}\right)$$

Simplificar

Gráfico

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Derivada de y=x^(sin2x)

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Definida a trozos:

Solución