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

Derivada de y=tan(×)^tan(x)

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

Gráfico:

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Definida a trozos:

Solución

Ha introducido [src] 
   tan(x)   
tan      (x)
tan⁡tan⁡(x)(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

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

Respuesta:

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

Gráfica
02468-8-6-4-2-10102e45-1e45
Trazar el gráfico f(x)
Trazar el gráfico f'(x)
Primera derivada [src] 
   tan(x)    /       2      /       2   \            \
tan      (x)*\1 + tan (x) + \1 + tan (x)/*log(tan(x))/
((tan⁡2(x)+1)log⁡(tan⁡(x))+tan⁡2(x)+1)tan⁡tan⁡(x)(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)}
Simplificar
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)                         //
((tan⁡2(x)+1)(tan⁡2(x)+1tan⁡(x)+2log⁡(tan⁡(x))tan⁡(x)+2tan⁡(x))+((tan⁡2(x)+1)log⁡(tan⁡(x))+tan⁡2(x)+1)2)tan⁡tan⁡(x)(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)}
Simplificar
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)                                                          /                                                                                                            /
(3(tan⁡2(x)+1)((tan⁡2(x)+1)log⁡(tan⁡(x))+tan⁡2(x)+1)(tan⁡2(x)+1tan⁡(x)+2log⁡(tan⁡(x))tan⁡(x)+2tan⁡(x))+(tan⁡2(x)+1)(−(tan⁡2(x)+1)2tan⁡2(x)+2(tan⁡2(x)+1)log⁡(tan⁡(x))+4log⁡(tan⁡(x))tan⁡2(x)+12tan⁡2(x)+8)+((tan⁡2(x)+1)log⁡(tan⁡(x))+tan⁡2(x)+1)3)tan⁡tan⁡(x)(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)}
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Gráfico
Derivada de y=tan(×)^tan(x)
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