Derivada de y=tgx^lnx

Ha introducido [src]

   log(x)   
tan      (x)

$$\tan^{\log{\left(x \right)}}{\left(x \right)}$$

tan(x)^log(x)

Solución detallada

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Perola derivada

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

Respuesta:

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

Gráfica

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Trazar el gráfico f'(x)

Primera derivada [src]

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

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

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Segunda derivada [src]

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

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

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Tercera derivada [src]

             /                                    3                                          /                                                    2                         \                                                    2                         2                                    3                                       \
             |/              /       2   \       \      /              /       2   \       \ |                                       /       2   \             /       2   \|                     /       2   \     /       2   \             /       2   \      /       2   \     /       2   \                                        |
   log(x)    ||log(tan(x))   \1 + tan (x)/*log(x)|      |log(tan(x))   \1 + tan (x)/*log(x)| |log(tan(x))     /       2   \          \1 + tan (x)/ *log(x)   2*\1 + tan (x)/|   2*log(tan(x))   6*\1 + tan (x)/   4*\1 + tan (x)/ *log(x)   3*\1 + tan (x)/    3*\1 + tan (x)/   2*\1 + tan (x)/ *log(x)     /       2   \              |
tan      (x)*||----------- + --------------------|  - 3*|----------- + --------------------|*|----------- - 2*\1 + tan (x)/*log(x) + --------------------- - ---------------| + ------------- + --------------- - ----------------------- - ---------------- - --------------- + ----------------------- + 4*\1 + tan (x)/*log(x)*tan(x)|
             |\     x               tan(x)       /      \     x               tan(x)       / |      2                                          2                 x*tan(x)   |          3               x                   tan(x)                   2              2                        3                                           |
             \                                                                               \     x                                        tan (x)                         /         x                                                        x*tan (x)          x *tan(x)              tan (x)                                        /

$$\left(\left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)}}{\tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x}\right) \left(\frac{\left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{\tan^{2}{\left(x \right)}} - 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} - \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)}{x \tan{\left(x \right)}} + \frac{\log{\left(\tan{\left(x \right)} \right)}}{x^{2}}\right) + \frac{2 \left(\tan^{2}{\left(x \right)} + 1\right)^{3} \log{\left(x \right)}}{\tan^{3}{\left(x \right)}} - \frac{4 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x \right)}}{\tan{\left(x \right)}} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x \right)} \tan{\left(x \right)} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{x \tan^{2}{\left(x \right)}} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x} - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} \tan{\left(x \right)}} + \frac{2 \log{\left(\tan{\left(x \right)} \right)}}{x^{3}}\right) \tan^{\log{\left(x \right)}}{\left(x \right)}$$

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Gráfico

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Derivada de y=tgx^lnx

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