Derivada de y=(lnx)^tg2x

Ha introducido [src]

   tan(2*x)   
log        (x)

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

log(x)^tan(2*x)

Solución detallada

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

Perola derivada

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

Respuesta:

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

Gráfica

Trazar el gráfico f(x)

Trazar el gráfico f'(x)

Primera derivada [src]

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

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

Simplificar

Segunda derivada [src]

               /                                          2                              /       2     \                                         \
   tan(2*x)    |/  /       2     \               tan(2*x)\     tan(2*x)    tan(2*x)    4*\1 + tan (2*x)/     /       2     \                     |
log        (x)*||2*\1 + tan (2*x)/*log(log(x)) + --------|  - --------- - ---------- + ----------------- + 8*\1 + tan (2*x)/*log(log(x))*tan(2*x)|
               |\                                x*log(x)/     2           2    2           x*log(x)                                             |
               \                                              x *log(x)   x *log (x)                                                             /

$$\left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} + \frac{\tan{\left(2 x \right)}}{x \log{\left(x \right)}}\right)^{2} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \tan{\left(2 x \right)} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \log{\left(x \right)}} - \frac{\tan{\left(2 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\tan{\left(2 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) \log{\left(x \right)}^{\tan{\left(2 x \right)}}$$

Simplificar

Tercera derivada [src]

               /                                          3                                                /                             /       2     \                                         \                     2                 /       2     \     /       2     \                                                                                        /       2     \         \
   tan(2*x)    |/  /       2     \               tan(2*x)\      /  /       2     \               tan(2*x)\ |   tan(2*x)    tan(2*x)    4*\1 + tan (2*x)/     /       2     \                     |      /       2     \                6*\1 + tan (2*x)/   6*\1 + tan (2*x)/   2*tan(2*x)   2*tan(2*x)   3*tan(2*x)         2      /       2     \               24*\1 + tan (2*x)/*tan(2*x)|
log        (x)*||2*\1 + tan (2*x)/*log(log(x)) + --------|  + 3*|2*\1 + tan (2*x)/*log(log(x)) + --------|*|- --------- - ---------- + ----------------- + 8*\1 + tan (2*x)/*log(log(x))*tan(2*x)| + 16*\1 + tan (2*x)/ *log(log(x)) - ----------------- - ----------------- + ---------- + ---------- + ---------- + 32*tan (2*x)*\1 + tan (2*x)/*log(log(x)) + ---------------------------|
               |\                                x*log(x)/      \                                x*log(x)/ |   2           2    2           x*log(x)                                             |                                          2                   2    2          3            3    3       3    2                                                           x*log(x)         |
               \                                                                                           \  x *log(x)   x *log (x)                                                             /                                         x *log(x)           x *log (x)      x *log(x)    x *log (x)   x *log (x)                                                                         /

$$\left(\left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} + \frac{\tan{\left(2 x \right)}}{x \log{\left(x \right)}}\right)^{3} + 3 \left(2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} + \frac{\tan{\left(2 x \right)}}{x \log{\left(x \right)}}\right) \left(8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \tan{\left(2 x \right)} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \log{\left(x \right)}} - \frac{\tan{\left(2 x \right)}}{x^{2} \log{\left(x \right)}} - \frac{\tan{\left(2 x \right)}}{x^{2} \log{\left(x \right)}^{2}}\right) + 16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(\log{\left(x \right)} \right)} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(\log{\left(x \right)} \right)} \tan^{2}{\left(2 x \right)} + \frac{24 \left(\tan^{2}{\left(2 x \right)} + 1\right) \tan{\left(2 x \right)}}{x \log{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{2} \log{\left(x \right)}} - \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{2} \log{\left(x \right)}^{2}} + \frac{2 \tan{\left(2 x \right)}}{x^{3} \log{\left(x \right)}} + \frac{3 \tan{\left(2 x \right)}}{x^{3} \log{\left(x \right)}^{2}} + \frac{2 \tan{\left(2 x \right)}}{x^{3} \log{\left(x \right)}^{3}}\right) \log{\left(x \right)}^{\tan{\left(2 x \right)}}$$

Simplificar

Gráfico

Otras calculadoras

¿Cómo usar?

Expresiones idénticas

Expresiones con funciones

Derivada de y=(lnx)^tg2x

Gráfico:

Definida a trozos:

Solución