Derivada de y=(tgx)^ln(6·x)

Ha introducido [src]

   log(6*x)   
tan        (x)

$$\tan^{\log{\left(6 x \right)}}{\left(x \right)}$$

tan(x)^log(6*x)

Solución detallada

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

Perola derivada

$\left(\log{\left(\log{\left(6 x \right)} \right)} + 1\right) \log{\left(6 x \right)}^{\log{\left(6 x \right)}}$

Respuesta:

$\left(\log{\left(\log{\left(6 x \right)} \right)} + 1\right) \log{\left(6 x \right)}^{\log{\left(6 x \right)}}$

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

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

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

Simplificar

Tercera derivada [src]

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

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

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de y=(tgx)^ln(6·x)

Gráfico:

Definida a trozos:

Solución