Sr Examen

Derivada de y=(tg2x)^cos⁡2x

Función f() - derivada -er orden en el punto
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Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
   cos(2*x)     
tan        (2*x)
$$\tan^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
tan(2*x)^cos(2*x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
                 /                            /         2     \         \
   cos(2*x)      |                            \2 + 2*tan (2*x)/*cos(2*x)|
tan        (2*x)*|-2*log(tan(2*x))*sin(2*x) + --------------------------|
                 \                                     tan(2*x)         /
$$\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \cos{\left(2 x \right)}}{\tan{\left(2 x \right)}} - 2 \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(2 x \right)}\right) \tan^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
Segunda derivada [src]
                   /                                                    2                                                                        2                                      \
                   |/                          /       2     \         \                                                          /       2     \               /       2     \         |
     cos(2*x)      ||                          \1 + tan (2*x)/*cos(2*x)|                               /       2     \            \1 + tan (2*x)/ *cos(2*x)   2*\1 + tan (2*x)/*sin(2*x)|
4*tan        (2*x)*||-log(tan(2*x))*sin(2*x) + ------------------------|  - cos(2*x)*log(tan(2*x)) + 2*\1 + tan (2*x)/*cos(2*x) - ------------------------- - --------------------------|
                   |\                                  tan(2*x)        /                                                                     2                         tan(2*x)         |
                   \                                                                                                                      tan (2*x)                                     /
$$4 \left(\left(\frac{\left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(2 x \right)}\right)^{2} - \frac{\left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(2 x \right)}} + 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)} - \log{\left(\tan{\left(2 x \right)} \right)} \cos{\left(2 x \right)}\right) \tan^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
Tercera derivada [src]
                   /                                                    3                                                                                                                /                                                                     2                                      \                    2                                                          3                             2                                               \
                   |/                          /       2     \         \                                                            /                          /       2     \         \ |                                                      /       2     \               /       2     \         |     /       2     \               /       2     \              /       2     \               /       2     \                                                |
     cos(2*x)      ||                          \1 + tan (2*x)/*cos(2*x)|                               /       2     \              |                          \1 + tan (2*x)/*cos(2*x)| |                           /       2     \            \1 + tan (2*x)/ *cos(2*x)   2*\1 + tan (2*x)/*sin(2*x)|   4*\1 + tan (2*x)/ *cos(2*x)   3*\1 + tan (2*x)/*cos(2*x)   2*\1 + tan (2*x)/ *cos(2*x)   3*\1 + tan (2*x)/ *sin(2*x)     /       2     \                  |
8*tan        (2*x)*||-log(tan(2*x))*sin(2*x) + ------------------------|  + log(tan(2*x))*sin(2*x) - 6*\1 + tan (2*x)/*sin(2*x) - 3*|-log(tan(2*x))*sin(2*x) + ------------------------|*|cos(2*x)*log(tan(2*x)) - 2*\1 + tan (2*x)/*cos(2*x) + ------------------------- + --------------------------| - --------------------------- - -------------------------- + --------------------------- + --------------------------- + 4*\1 + tan (2*x)/*cos(2*x)*tan(2*x)|
                   |\                                  tan(2*x)        /                                                            \                                  tan(2*x)        / |                                                                 2                         tan(2*x)         |             tan(2*x)                     tan(2*x)                        3                             2                                                    |
                   \                                                                                                                                                                     \                                                              tan (2*x)                                     /                                                                       tan (2*x)                     tan (2*x)                                               /
$$8 \left(\left(\frac{\left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(2 x \right)}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(2 x \right)}} - \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(2 x \right)}\right) \left(\frac{\left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)}} + \frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sin{\left(2 x \right)}}{\tan{\left(2 x \right)}} - 2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)} + \log{\left(\tan{\left(2 x \right)} \right)} \cos{\left(2 x \right)}\right) + \frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \cos{\left(2 x \right)}}{\tan^{3}{\left(2 x \right)}} + \frac{3 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \sin{\left(2 x \right)}}{\tan^{2}{\left(2 x \right)}} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \cos{\left(2 x \right)}}{\tan{\left(2 x \right)}} - 6 \left(\tan^{2}{\left(2 x \right)} + 1\right) \sin{\left(2 x \right)} + 4 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)} \tan{\left(2 x \right)} - \frac{3 \left(\tan^{2}{\left(2 x \right)} + 1\right) \cos{\left(2 x \right)}}{\tan{\left(2 x \right)}} + \log{\left(\tan{\left(2 x \right)} \right)} \sin{\left(2 x \right)}\right) \tan^{\cos{\left(2 x \right)}}{\left(2 x \right)}$$
Gráfico
Derivada de y=(tg2x)^cos⁡2x