Derivada de y=(cos2x)^e^sinx

Ha introducido [src]

          / sin(x)\
          \E      /
(cos(2*x))

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

cos(2*x)^(E^sin(x))

Solución detallada

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

Perola derivada

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

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

          / sin(x)\ /                                                3                                                                                3              2                    2                                                     /                                                        2                         \                                                            \        
          \e      / |             /                       2*sin(2*x)\   2*sin(x)      3                                           16*sin(2*x)   16*sin (2*x)   12*sin (2*x)*cos(x)   6*cos (x)*sin(2*x)     /                       2*sin(2*x)\ |                              2                    4*sin (2*x)   4*cos(x)*sin(2*x)|  sin(x)                                   6*sin(x)*sin(2*x)|  sin(x)
(cos(2*x))         *|-12*cos(x) + |cos(x)*log(cos(2*x)) - ----------| *e         + cos (x)*log(cos(2*x)) - cos(x)*log(cos(2*x)) - ----------- - ------------ - ------------------- - ------------------ - 3*|cos(x)*log(cos(2*x)) - ----------|*|4 + log(cos(2*x))*sin(x) - cos (x)*log(cos(2*x)) + ----------- + -----------------|*e       - 3*cos(x)*log(cos(2*x))*sin(x) + -----------------|*e      
                    |             \                        cos(2*x) /                                                               cos(2*x)        3                  2                  cos(2*x)          \                        cos(2*x) / |                                                       2              cos(2*x)    |                                                cos(2*x)    |        
                    \                                                                                                                            cos (2*x)          cos (2*x)                                                                   \                                                    cos (2*x)                     /                                                            /

$$\left(\left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right)^{3} e^{2 \sin{\left(x \right)}} - 3 \left(\log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} - \frac{2 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}}\right) \left(\log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} - \log{\left(\cos{\left(2 x \right)} \right)} \cos^{2}{\left(x \right)} + \frac{4 \sin^{2}{\left(2 x \right)}}{\cos^{2}{\left(2 x \right)}} + \frac{4 \sin{\left(2 x \right)} \cos{\left(x \right)}}{\cos{\left(2 x \right)}} + 4\right) e^{\sin{\left(x \right)}} - 3 \log{\left(\cos{\left(2 x \right)} \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \log{\left(\cos{\left(2 x \right)} \right)} \cos^{3}{\left(x \right)} - \log{\left(\cos{\left(2 x \right)} \right)} \cos{\left(x \right)} + \frac{6 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} - \frac{16 \sin^{3}{\left(2 x \right)}}{\cos^{3}{\left(2 x \right)}} - \frac{12 \sin^{2}{\left(2 x \right)} \cos{\left(x \right)}}{\cos^{2}{\left(2 x \right)}} - \frac{6 \sin{\left(2 x \right)} \cos^{2}{\left(x \right)}}{\cos{\left(2 x \right)}} - \frac{16 \sin{\left(2 x \right)}}{\cos{\left(2 x \right)}} - 12 \cos{\left(x \right)}\right) e^{\sin{\left(x \right)}} \cos^{e^{\sin{\left(x \right)}}}{\left(2 x \right)}$$

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Gráfico

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Derivada de y=(cos2x)^e^sinx

Gráfico:

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Solución