Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ / 2 \ \
x |x*\1 + tan (x)/ |
tan (x)*|--------------- + log(tan(x))|
\ tan(x) /
$$\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \tan^{x}{\left(x \right)}$$
/ 2 \
|/ / 2 \ \ / / 2 \\|
x ||x*\1 + tan (x)/ | / 2 \ | 2 x*\1 + tan (x)/||
tan (x)*||--------------- + log(tan(x))| + \1 + tan (x)/*|2*x + ------ - ---------------||
|\ tan(x) / | tan(x) 2 ||
\ \ tan (x) //
$$\left(\left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{2} + \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 x + \frac{2}{\tan{\left(x \right)}}\right)\right) \tan^{x}{\left(x \right)}$$
/ 3 2 2 3 \
| / / 2 \ \ / 2 \ / 2 \ / 2 \ / / 2 \ \ / / 2 \\ |
x | |x*\1 + tan (x)/ | 2 3*\1 + tan (x)/ 4*x*\1 + tan (x)/ 2*x*\1 + tan (x)/ / 2 \ |x*\1 + tan (x)/ | | 2 x*\1 + tan (x)/| / 2 \ |
tan (x)*|6 + |--------------- + log(tan(x))| + 6*tan (x) - ---------------- - ------------------ + ------------------ + 3*\1 + tan (x)/*|--------------- + log(tan(x))|*|2*x + ------ - ---------------| + 4*x*\1 + tan (x)/*tan(x)|
| \ tan(x) / 2 tan(x) 3 \ tan(x) / | tan(x) 2 | |
\ tan (x) tan (x) \ tan (x) / /
$$\left(\frac{2 x \left(\tan^{2}{\left(x \right)} + 1\right)^{3}}{\tan^{3}{\left(x \right)}} - \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan{\left(x \right)}} + 4 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)} + \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right)^{3} + 3 \left(\frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan{\left(x \right)}} + \log{\left(\tan{\left(x \right)} \right)}\right) \left(\tan^{2}{\left(x \right)} + 1\right) \left(- \frac{x \left(\tan^{2}{\left(x \right)} + 1\right)}{\tan^{2}{\left(x \right)}} + 2 x + \frac{2}{\tan{\left(x \right)}}\right) - \frac{3 \left(\tan^{2}{\left(x \right)} + 1\right)^{2}}{\tan^{2}{\left(x \right)}} + 6 \tan^{2}{\left(x \right)} + 6\right) \tan^{x}{\left(x \right)}$$