Sr Examen

Derivada de y=(tg2x)^(tg2x)

Función f() - derivada -er orden en el punto
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Gráfico:

interior superior

Definida a trozos:

Solución

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

    Perola derivada


Respuesta:

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