Derivada de y=(cos(6x))^tg(x)

Ha introducido [src]

   tan(x)     
cos      (6*x)

$$\cos^{\tan{\left(x \right)}}{\left(6 x \right)}$$

cos(6*x)^tan(x)

Solución detallada

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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

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Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

               /                                                 2                     2                  /       2   \                                                \
   tan(x)      |//       2   \                 6*sin(6*x)*tan(x)\                36*sin (6*x)*tan(x)   12*\1 + tan (x)/*sin(6*x)     /       2   \                     |
cos      (6*x)*||\1 + tan (x)/*log(cos(6*x)) - -----------------|  - 36*tan(x) - ------------------- - ------------------------- + 2*\1 + tan (x)/*log(cos(6*x))*tan(x)|
               |\                                   cos(6*x)    /                        2                      cos(6*x)                                               |
               \                                                                      cos (6*x)                                                                        /

$$\left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(6 x \right)} \right)} - \frac{6 \sin{\left(6 x \right)} \tan{\left(x \right)}}{\cos{\left(6 x \right)}}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(6 x \right)} \right)} \tan{\left(x \right)} - \frac{12 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} - \frac{36 \sin^{2}{\left(6 x \right)} \tan{\left(x \right)}}{\cos^{2}{\left(6 x \right)}} - 36 \tan{\left(x \right)}\right) \cos^{\tan{\left(x \right)}}{\left(6 x \right)}$$

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Tercera derivada [src]

               /                                                        3                                                                     /                                                   /       2   \                  2            \                  2                                              3                      2      /       2   \                                              /       2   \                \
   tan(x)      |       //       2   \                 6*sin(6*x)*tan(x)\           2        //       2   \                 6*sin(6*x)*tan(x)\ |            /       2   \                        6*\1 + tan (x)/*sin(6*x)   18*sin (6*x)*tan(x)|     /       2   \                  432*sin(6*x)*tan(x)   432*sin (6*x)*tan(x)   108*sin (6*x)*\1 + tan (x)/        2    /       2   \                 36*\1 + tan (x)/*sin(6*x)*tan(x)|
cos      (6*x)*|-108 + |\1 + tan (x)/*log(cos(6*x)) - -----------------|  - 108*tan (x) - 6*|\1 + tan (x)/*log(cos(6*x)) - -----------------|*|18*tan(x) - \1 + tan (x)/*log(cos(6*x))*tan(x) + ------------------------ + -------------------| + 2*\1 + tan (x)/ *log(cos(6*x)) - ------------------- - -------------------- - --------------------------- + 4*tan (x)*\1 + tan (x)/*log(cos(6*x)) - --------------------------------|
               |       \                                   cos(6*x)    /                    \                                   cos(6*x)    / |                                                         cos(6*x)                   2          |                                          cos(6*x)                3                          2                                                                     cos(6*x)            |
               \                                                                                                                              \                                                                                 cos (6*x)     /                                                               cos (6*x)                  cos (6*x)                                                                                    /

$$\left(\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(6 x \right)} \right)} - \frac{6 \sin{\left(6 x \right)} \tan{\left(x \right)}}{\cos{\left(6 x \right)}}\right)^{3} - 6 \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(6 x \right)} \right)} - \frac{6 \sin{\left(6 x \right)} \tan{\left(x \right)}}{\cos{\left(6 x \right)}}\right) \left(- \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(6 x \right)} \right)} \tan{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(6 x \right)}}{\cos{\left(6 x \right)}} + \frac{18 \sin^{2}{\left(6 x \right)} \tan{\left(x \right)}}{\cos^{2}{\left(6 x \right)}} + 18 \tan{\left(x \right)}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(\cos{\left(6 x \right)} \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\cos{\left(6 x \right)} \right)} \tan^{2}{\left(x \right)} - \frac{108 \left(\tan^{2}{\left(x \right)} + 1\right) \sin^{2}{\left(6 x \right)}}{\cos^{2}{\left(6 x \right)}} - \frac{36 \left(\tan^{2}{\left(x \right)} + 1\right) \sin{\left(6 x \right)} \tan{\left(x \right)}}{\cos{\left(6 x \right)}} - \frac{432 \sin^{3}{\left(6 x \right)} \tan{\left(x \right)}}{\cos^{3}{\left(6 x \right)}} - \frac{432 \sin{\left(6 x \right)} \tan{\left(x \right)}}{\cos{\left(6 x \right)}} - 108 \tan^{2}{\left(x \right)} - 108\right) \cos^{\tan{\left(x \right)}}{\left(6 x \right)}$$

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Derivada de y=(cos(6x))^tg(x)

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