Derivada de y=(1-cos(5*x))^sinx

Ha introducido [src]

              sin(x)
(1 - cos(5*x))

$$\left(1 - \cos{\left(5 x \right)}\right)^{\sin{\left(x \right)}}$$

(1 - cos(5*x))^sin(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

              sin(x) /                           5*sin(x)*sin(5*x)\
(1 - cos(5*x))      *|cos(x)*log(1 - cos(5*x)) + -----------------|
                     \                              1 - cos(5*x)  /

$$\left(1 - \cos{\left(5 x \right)}\right)^{\sin{\left(x \right)}} \left(\log{\left(1 - \cos{\left(5 x \right)} \right)} \cos{\left(x \right)} + \frac{5 \sin{\left(x \right)} \sin{\left(5 x \right)}}{1 - \cos{\left(5 x \right)}}\right)$$

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Segunda derivada [src]

                     /                                              2                                                         2                                 \
              sin(x) |/                           5*sin(x)*sin(5*x)\                               25*cos(5*x)*sin(x)   25*sin (5*x)*sin(x)   10*cos(x)*sin(5*x)|
(1 - cos(5*x))      *||cos(x)*log(1 - cos(5*x)) - -----------------|  - log(1 - cos(5*x))*sin(x) - ------------------ - ------------------- - ------------------|
                     |\                             -1 + cos(5*x)  /                                 -1 + cos(5*x)                       2      -1 + cos(5*x)   |
                     \                                                                                                    (-1 + cos(5*x))                       /

$$\left(1 - \cos{\left(5 x \right)}\right)^{\sin{\left(x \right)}} \left(\left(\log{\left(1 - \cos{\left(5 x \right)} \right)} \cos{\left(x \right)} - \frac{5 \sin{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1}\right)^{2} - \log{\left(1 - \cos{\left(5 x \right)} \right)} \sin{\left(x \right)} - \frac{25 \sin{\left(x \right)} \cos{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1} - \frac{10 \sin{\left(5 x \right)} \cos{\left(x \right)}}{\cos{\left(5 x \right)} - 1} - \frac{25 \sin{\left(x \right)} \sin^{2}{\left(5 x \right)}}{\left(\cos{\left(5 x \right)} - 1\right)^{2}}\right)$$

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Tercera derivada [src]

                     /                                              3                                                                               /                                                                           2            \          3                                          2                                                                 \
              sin(x) |/                           5*sin(x)*sin(5*x)\                                 /                           5*sin(x)*sin(5*x)\ |                           10*cos(x)*sin(5*x)   25*cos(5*x)*sin(x)   25*sin (5*x)*sin(x)|   250*sin (5*x)*sin(x)   75*cos(x)*cos(5*x)   75*sin (5*x)*cos(x)   140*sin(x)*sin(5*x)   375*cos(5*x)*sin(x)*sin(5*x)|
(1 - cos(5*x))      *||cos(x)*log(1 - cos(5*x)) - -----------------|  - cos(x)*log(1 - cos(5*x)) - 3*|cos(x)*log(1 - cos(5*x)) - -----------------|*|log(1 - cos(5*x))*sin(x) + ------------------ + ------------------ + -------------------| - -------------------- - ------------------ - ------------------- + ------------------- - ----------------------------|
                     |\                             -1 + cos(5*x)  /                                 \                             -1 + cos(5*x)  / |                             -1 + cos(5*x)        -1 + cos(5*x)                       2 |                    3       -1 + cos(5*x)                       2       -1 + cos(5*x)                           2      |
                     \                                                                                                                              \                                                                       (-1 + cos(5*x))  /     (-1 + cos(5*x))                             (-1 + cos(5*x))                                 (-1 + cos(5*x))       /

$$\left(1 - \cos{\left(5 x \right)}\right)^{\sin{\left(x \right)}} \left(\left(\log{\left(1 - \cos{\left(5 x \right)} \right)} \cos{\left(x \right)} - \frac{5 \sin{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1}\right)^{3} - 3 \left(\log{\left(1 - \cos{\left(5 x \right)} \right)} \cos{\left(x \right)} - \frac{5 \sin{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1}\right) \left(\log{\left(1 - \cos{\left(5 x \right)} \right)} \sin{\left(x \right)} + \frac{25 \sin{\left(x \right)} \cos{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1} + \frac{10 \sin{\left(5 x \right)} \cos{\left(x \right)}}{\cos{\left(5 x \right)} - 1} + \frac{25 \sin{\left(x \right)} \sin^{2}{\left(5 x \right)}}{\left(\cos{\left(5 x \right)} - 1\right)^{2}}\right) - \log{\left(1 - \cos{\left(5 x \right)} \right)} \cos{\left(x \right)} + \frac{140 \sin{\left(x \right)} \sin{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1} - \frac{75 \cos{\left(x \right)} \cos{\left(5 x \right)}}{\cos{\left(5 x \right)} - 1} - \frac{375 \sin{\left(x \right)} \sin{\left(5 x \right)} \cos{\left(5 x \right)}}{\left(\cos{\left(5 x \right)} - 1\right)^{2}} - \frac{75 \sin^{2}{\left(5 x \right)} \cos{\left(x \right)}}{\left(\cos{\left(5 x \right)} - 1\right)^{2}} - \frac{250 \sin{\left(x \right)} \sin^{3}{\left(5 x \right)}}{\left(\cos{\left(5 x \right)} - 1\right)^{3}}\right)$$

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Derivada de y=(1-cos(5*x))^sinx

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