Sr Examen

Derivada de y=(tg2x)^lnx

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

Gráfico:

interior superior

Definida a trozos:

Solución

Ha introducido [src]
   log(x)     
tan      (2*x)
$$\tan^{\log{\left(x \right)}}{\left(2 x \right)}$$
tan(2*x)^log(x)
Solución detallada
  1. No logro encontrar los pasos en la búsqueda de esta derivada.

    Perola derivada


Respuesta:

Gráfica
Primera derivada [src]
               /                /         2     \       \
   log(x)      |log(tan(2*x))   \2 + 2*tan (2*x)/*log(x)|
tan      (2*x)*|------------- + ------------------------|
               \      x                 tan(2*x)        /
$$\left(\frac{\left(2 \tan^{2}{\left(2 x \right)} + 2\right) \log{\left(x \right)}}{\tan{\left(2 x \right)}} + \frac{\log{\left(\tan{\left(2 x \right)} \right)}}{x}\right) \tan^{\log{\left(x \right)}}{\left(2 x \right)}$$
Segunda derivada [src]
               /                                          2                                                               2                           \
               |/                  /       2     \       \                                                 /       2     \             /       2     \|
   log(x)      ||log(tan(2*x))   2*\1 + tan (2*x)/*log(x)|    log(tan(2*x))     /       2     \          4*\1 + tan (2*x)/ *log(x)   4*\1 + tan (2*x)/|
tan      (2*x)*||------------- + ------------------------|  - ------------- + 8*\1 + tan (2*x)/*log(x) - ------------------------- + -----------------|
               |\      x                 tan(2*x)        /           2                                              2                    x*tan(2*x)   |
               \                                                    x                                            tan (2*x)                            /
$$\left(\left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)}}{\tan{\left(2 x \right)}} + \frac{\log{\left(\tan{\left(2 x \right)} \right)}}{x}\right)^{2} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} + 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} + \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \tan{\left(2 x \right)}} - \frac{\log{\left(\tan{\left(2 x \right)} \right)}}{x^{2}}\right) \tan^{\log{\left(x \right)}}{\left(2 x \right)}$$
Tercera derivada [src]
               /                                          3                                                /                                                                                2       \                                                            2                            2                                         3                                            \
               |/                  /       2     \       \      /                  /       2     \       \ |                                             /       2     \     /       2     \        |                        /       2     \      /       2     \              /       2     \      /       2     \      /       2     \                                             |
   log(x)      ||log(tan(2*x))   2*\1 + tan (2*x)/*log(x)|      |log(tan(2*x))   2*\1 + tan (2*x)/*log(x)| |log(tan(2*x))     /       2     \          4*\1 + tan (2*x)/   4*\1 + tan (2*x)/ *log(x)|   2*log(tan(2*x))   24*\1 + tan (2*x)/   32*\1 + tan (2*x)/ *log(x)   12*\1 + tan (2*x)/    6*\1 + tan (2*x)/   16*\1 + tan (2*x)/ *log(x)      /       2     \                |
tan      (2*x)*||------------- + ------------------------|  - 3*|------------- + ------------------------|*|------------- - 8*\1 + tan (2*x)/*log(x) - ----------------- + -------------------------| + --------------- + ------------------ - -------------------------- - ------------------- - ----------------- + -------------------------- + 32*\1 + tan (2*x)/*log(x)*tan(2*x)|
               |\      x                 tan(2*x)        /      \      x                 tan(2*x)        / |       2                                       x*tan(2*x)                 2             |           3                 x                     tan(2*x)                     2                2                          3                                                   |
               \                                                                                           \      x                                                                tan (2*x)        /          x                                                                x*tan (2*x)          x *tan(2*x)              tan (2*x)                                              /
$$\left(\left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)}}{\tan{\left(2 x \right)}} + \frac{\log{\left(\tan{\left(2 x \right)} \right)}}{x}\right)^{3} - 3 \left(\frac{2 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)}}{\tan{\left(2 x \right)}} + \frac{\log{\left(\tan{\left(2 x \right)} \right)}}{x}\right) \left(\frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x \right)}}{\tan^{2}{\left(2 x \right)}} - 8 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} - \frac{4 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x \tan{\left(2 x \right)}} + \frac{\log{\left(\tan{\left(2 x \right)} \right)}}{x^{2}}\right) + \frac{16 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{3} \log{\left(x \right)}}{\tan^{3}{\left(2 x \right)}} - \frac{32 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2} \log{\left(x \right)}}{\tan{\left(2 x \right)}} + 32 \left(\tan^{2}{\left(2 x \right)} + 1\right) \log{\left(x \right)} \tan{\left(2 x \right)} - \frac{12 \left(\tan^{2}{\left(2 x \right)} + 1\right)^{2}}{x \tan^{2}{\left(2 x \right)}} + \frac{24 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x} - \frac{6 \left(\tan^{2}{\left(2 x \right)} + 1\right)}{x^{2} \tan{\left(2 x \right)}} + \frac{2 \log{\left(\tan{\left(2 x \right)} \right)}}{x^{3}}\right) \tan^{\log{\left(x \right)}}{\left(2 x \right)}$$
Gráfico
Derivada de y=(tg2x)^lnx