Sr Examen

Derivada de y=tan(×)^tan(x)

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

Gráfico:

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Solución

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

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
   tan(x)    /       2      /       2   \            \
tan      (x)*\1 + tan (x) + \1 + tan (x)/*log(tan(x))/
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} + \tan^{2}{\left(x \right)} + 1\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$$
Segunda derivada [src]
             /                                         2                 /                  2                          \\
   tan(x)    |/       2      /       2   \            \    /       2   \ |           1 + tan (x)                       ||
tan      (x)*|\1 + tan (x) + \1 + tan (x)/*log(tan(x))/  + \1 + tan (x)/*|2*tan(x) + ----------- + 2*log(tan(x))*tan(x)||
             \                                                           \              tan(x)                         //
$$\left(\left(\tan^{2}{\left(x \right)} + 1\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} + 2 \tan{\left(x \right)}\right) + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} + \tan^{2}{\left(x \right)} + 1\right)^{2}\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$$
Tercera derivada [src]
             /                                                           /                              2                                                      \                                                                                                            \
             |                                         3                 |                 /       2   \                                                       |                                                             /                  2                          \|
   tan(x)    |/       2      /       2   \            \    /       2   \ |          2      \1 + tan (x)/      /       2   \                    2               |     /       2   \ /       2      /       2   \            \ |           1 + tan (x)                       ||
tan      (x)*|\1 + tan (x) + \1 + tan (x)/*log(tan(x))/  + \1 + tan (x)/*|8 + 12*tan (x) - -------------- + 2*\1 + tan (x)/*log(tan(x)) + 4*tan (x)*log(tan(x))| + 3*\1 + tan (x)/*\1 + tan (x) + \1 + tan (x)/*log(tan(x))/*|2*tan(x) + ----------- + 2*log(tan(x))*tan(x)||
             |                                                           |                       2                                                             |                                                             \              tan(x)                         /|
             \                                                           \                    tan (x)                                                          /                                                                                                            /
$$\left(3 \left(\tan^{2}{\left(x \right)} + 1\right) \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} + \tan^{2}{\left(x \right)} + 1\right) \left(\frac{\tan^{2}{\left(x \right)} + 1}{\tan{\left(x \right)}} + 2 \log{\left(\tan{\left(x \right)} \right)} \tan{\left(x \right)} + 2 \tan{\left(x \right)}\right) + \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} + 4 \log{\left(\tan{\left(x \right)} \right)} \tan^{2}{\left(x \right)} + 12 \tan^{2}{\left(x \right)} + 8\right) + \left(\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(\tan{\left(x \right)} \right)} + \tan^{2}{\left(x \right)} + 1\right)^{3}\right) \tan^{\tan{\left(x \right)}}{\left(x \right)}$$
Gráfico
Derivada de y=tan(×)^tan(x)