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y=tan(cos(x))^x
Derivada de la función/ y=tan/ cos(x)/ y=tan(cos(x))^x

Derivada de y=tan(cos(x))^x

Función f() - derivada -er orden en el punto
v

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   x        
tan (cos(x))
tan⁡x(cos⁡(x))\tan^{x}{\left(\cos{\left(x \right)} \right)} 
tan(cos(x))^x
Solución detallada

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

    Perola derivada

    xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

Respuesta:

xx(log⁡(x)+1)x^{x} \left(\log{\left(x \right)} + 1\right)

Gráfica
02468-8-6-4-2-1010-10000000000050000000000
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
             /    /       2        \                          \
   x         |  x*\1 + tan (cos(x))/*sin(x)                   |
tan (cos(x))*|- --------------------------- + log(tan(cos(x)))|
             \          tan(cos(x))                           /
(−x(tan⁡2(cos⁡(x))+1)sin⁡(x)tan⁡(cos⁡(x))+log⁡(tan⁡(cos⁡(x))))tan⁡x(cos⁡(x))\left(- \frac{x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} + \log{\left(\tan{\left(\cos{\left(x \right)} \right)} \right)}\right) \tan^{x}{\left(\cos{\left(x \right)} \right)}
Simplificar
Segunda derivada [src] 
             /                                                 2                                                                                                \
             |/                      /       2        \       \                       /                                                 2    /       2        \\|
   x         ||                    x*\1 + tan (cos(x))/*sin(x)|    /       2        \ |         2        2*sin(x)      x*cos(x)    x*sin (x)*\1 + tan (cos(x))/||
tan (cos(x))*||-log(tan(cos(x))) + ---------------------------|  - \1 + tan (cos(x))/*|- 2*x*sin (x) + ----------- + ----------- + ----------------------------||
             |\                            tan(cos(x))        /                       |                tan(cos(x))   tan(cos(x))              2                ||
             \                                                                        \                                                    tan (cos(x))        //
((x(tan⁡2(cos⁡(x))+1)sin⁡(x)tan⁡(cos⁡(x))−log⁡(tan⁡(cos⁡(x))))2−(tan⁡2(cos⁡(x))+1)(x(tan⁡2(cos⁡(x))+1)sin⁡2(x)tan⁡2(cos⁡(x))−2xsin⁡2(x)+xcos⁡(x)tan⁡(cos⁡(x))+2sin⁡(x)tan⁡(cos⁡(x))))tan⁡x(cos⁡(x))\left(\left(\frac{x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} - \log{\left(\tan{\left(\cos{\left(x \right)} \right)} \right)}\right)^{2} - \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \left(\frac{x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin^{2}{\left(x \right)}}{\tan^{2}{\left(\cos{\left(x \right)} \right)}} - 2 x \sin^{2}{\left(x \right)} + \frac{x \cos{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} + \frac{2 \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}}\right)\right) \tan^{x}{\left(\cos{\left(x \right)} \right)}
Simplificar
Tercera derivada [src] 
             /                                                   3                      /                                                                                                                                                                              2                                               \                                                                                                                                                    \
             |  /                      /       2        \       \                       |                                                                   2    /       2        \                                    3    /       2        \       /       2        \     3          /       2        \              |                        /                      /       2        \       \ /                                                 2    /       2        \\|
   x         |  |                    x*\1 + tan (cos(x))/*sin(x)|    /       2        \ |       2        3*cos(x)      x*sin(x)                        3*sin (x)*\1 + tan (cos(x))/          3                  4*x*sin (x)*\1 + tan (cos(x))/   2*x*\1 + tan (cos(x))/ *sin (x)   3*x*\1 + tan (cos(x))/*cos(x)*sin(x)|     /       2        \ |                    x*\1 + tan (cos(x))/*sin(x)| |         2        2*sin(x)      x*cos(x)    x*sin (x)*\1 + tan (cos(x))/||
tan (cos(x))*|- |-log(tan(cos(x))) + ---------------------------|  - \1 + tan (cos(x))/*|- 6*sin (x) + ----------- - ----------- - 6*x*cos(x)*sin(x) + ---------------------------- + 4*x*sin (x)*tan(cos(x)) - ------------------------------ + ------------------------------- + ------------------------------------| + 3*\1 + tan (cos(x))/*|-log(tan(cos(x))) + ---------------------------|*|- 2*x*sin (x) + ----------- + ----------- + ----------------------------||
             |  \                            tan(cos(x))        /                       |              tan(cos(x))   tan(cos(x))                                  2                                                      tan(cos(x))                          3                                   2                    |                        \                            tan(cos(x))        / |                tan(cos(x))   tan(cos(x))              2                ||
             \                                                                          \                                                                      tan (cos(x))                                                                                tan (cos(x))                        tan (cos(x))            /                                                                          \                                                    tan (cos(x))        //
(−(x(tan⁡2(cos⁡(x))+1)sin⁡(x)tan⁡(cos⁡(x))−log⁡(tan⁡(cos⁡(x))))3+3(x(tan⁡2(cos⁡(x))+1)sin⁡(x)tan⁡(cos⁡(x))−log⁡(tan⁡(cos⁡(x))))(tan⁡2(cos⁡(x))+1)(x(tan⁡2(cos⁡(x))+1)sin⁡2(x)tan⁡2(cos⁡(x))−2xsin⁡2(x)+xcos⁡(x)tan⁡(cos⁡(x))+2sin⁡(x)tan⁡(cos⁡(x)))−(tan⁡2(cos⁡(x))+1)(2x(tan⁡2(cos⁡(x))+1)2sin⁡3(x)tan⁡3(cos⁡(x))−4x(tan⁡2(cos⁡(x))+1)sin⁡3(x)tan⁡(cos⁡(x))+3x(tan⁡2(cos⁡(x))+1)sin⁡(x)cos⁡(x)tan⁡2(cos⁡(x))+4xsin⁡3(x)tan⁡(cos⁡(x))−6xsin⁡(x)cos⁡(x)−xsin⁡(x)tan⁡(cos⁡(x))+3(tan⁡2(cos⁡(x))+1)sin⁡2(x)tan⁡2(cos⁡(x))−6sin⁡2(x)+3cos⁡(x)tan⁡(cos⁡(x))))tan⁡x(cos⁡(x))\left(- \left(\frac{x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} - \log{\left(\tan{\left(\cos{\left(x \right)} \right)} \right)}\right)^{3} + 3 \left(\frac{x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} - \log{\left(\tan{\left(\cos{\left(x \right)} \right)} \right)}\right) \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \left(\frac{x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin^{2}{\left(x \right)}}{\tan^{2}{\left(\cos{\left(x \right)} \right)}} - 2 x \sin^{2}{\left(x \right)} + \frac{x \cos{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} + \frac{2 \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}}\right) - \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \left(\frac{2 x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right)^{2} \sin^{3}{\left(x \right)}}{\tan^{3}{\left(\cos{\left(x \right)} \right)}} - \frac{4 x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin^{3}{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} + \frac{3 x \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin{\left(x \right)} \cos{\left(x \right)}}{\tan^{2}{\left(\cos{\left(x \right)} \right)}} + 4 x \sin^{3}{\left(x \right)} \tan{\left(\cos{\left(x \right)} \right)} - 6 x \sin{\left(x \right)} \cos{\left(x \right)} - \frac{x \sin{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}} + \frac{3 \left(\tan^{2}{\left(\cos{\left(x \right)} \right)} + 1\right) \sin^{2}{\left(x \right)}}{\tan^{2}{\left(\cos{\left(x \right)} \right)}} - 6 \sin^{2}{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{\tan{\left(\cos{\left(x \right)} \right)}}\right)\right) \tan^{x}{\left(\cos{\left(x \right)} \right)}
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Gráfico
Derivada de y=tan(cos(x))^x
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