Derivada de (cos(x))^tg(x)

Ha introducido [src]

   tan(x)   
cos      (x)

$$\cos^{\tan{\left(x \right)}}{\left(x \right)}$$

cos(x)^tan(x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

   tan(x)    //       2   \               sin(x)*tan(x)\
cos      (x)*|\1 + tan (x)/*log(cos(x)) - -------------|
             \                                cos(x)   /

$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} - \frac{\sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}}\right) \cos^{\tan{\left(x \right)}}{\left(x \right)}$$

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Segunda derivada [src]

             /                                           2               2               /       2   \                                            \
   tan(x)    |//       2   \               sin(x)*tan(x)\             sin (x)*tan(x)   2*\1 + tan (x)/*sin(x)     /       2   \                   |
cos      (x)*||\1 + tan (x)/*log(cos(x)) - -------------|  - tan(x) - -------------- - ---------------------- + 2*\1 + tan (x)/*log(cos(x))*tan(x)|
             |\                                cos(x)   /                   2                  cos(x)                                             |
             \                                                           cos (x)                                                                  /

$$\left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} - \frac{\sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} - \frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \tan{\left(x \right)}\right) \cos^{\tan{\left(x \right)}}{\left(x \right)}$$

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Tercera derivada [src]

             /                                                3                                                             /   2                                                    /       2   \                \                  2                    2    /       2   \                          3                                                     /       2   \              \
   tan(x)    |     //       2   \               sin(x)*tan(x)\         2        //       2   \               sin(x)*tan(x)\ |sin (x)*tan(x)     /       2   \                      2*\1 + tan (x)/*sin(x)         |     /       2   \                3*sin (x)*\1 + tan (x)/   2*sin(x)*tan(x)   2*sin (x)*tan(x)        2    /       2   \               6*\1 + tan (x)/*sin(x)*tan(x)|
cos      (x)*|-3 + |\1 + tan (x)/*log(cos(x)) - -------------|  - 3*tan (x) - 3*|\1 + tan (x)/*log(cos(x)) - -------------|*|-------------- - 2*\1 + tan (x)/*log(cos(x))*tan(x) + ---------------------- + tan(x)| + 2*\1 + tan (x)/ *log(cos(x)) - ----------------------- - --------------- - ---------------- + 4*tan (x)*\1 + tan (x)/*log(cos(x)) - -----------------------------|
             |     \                                cos(x)   /                  \                                cos(x)   / |      2                                                       cos(x)                 |                                             2                   cos(x)              3                                                             cos(x)           |
             \                                                                                                              \   cos (x)                                                                           /                                          cos (x)                                 cos (x)                                                                           /

$$\left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} - \frac{\sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}}\right)^{3} - 3 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} - \frac{\sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}}\right) \left(- 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} \tan{\left(x \right)} + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)}}{\cos{\left(x \right)}} + \frac{\sin^{2}{\left(x \right)} \tan{\left(x \right)}}{\cos^{2}{\left(x \right)}} + \tan{\left(x \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(x \right)} \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(x \right)} \right)} \tan^{2}{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right) \sin^{2}{\left(x \right)}}{\cos^{2}{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}} - \frac{2 \sin^{3}{\left(x \right)} \tan{\left(x \right)}}{\cos^{3}{\left(x \right)}} - \frac{2 \sin{\left(x \right)} \tan{\left(x \right)}}{\cos{\left(x \right)}} - 3 \tan^{2}{\left(x \right)} - 3\right) \cos^{\tan{\left(x \right)}}{\left(x \right)}$$

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Gráfico

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Derivada de (cos(x))^tg(x)

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