Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
tan(x) // 2 \ 2*x*tan(x)\
(x*x + 1) *|\1 + tan (x)/*log(x*x + 1) + ----------|
\ x*x + 1 /
$$\left(x x + 1\right)^{\tan{\left(x \right)}} \left(\frac{2 x \tan{\left(x \right)}}{x x + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x x + 1 \right)}\right)$$
tan(x) / 2 2 / 2 \\
/ 2\ |// 2 \ / 2\ 2*x*tan(x)\ 2*tan(x) 4*x *tan(x) / 2 \ / 2\ 4*x*\1 + tan (x)/|
\1 + x / *||\1 + tan (x)/*log\1 + x / + ----------| + -------- - ----------- + 2*\1 + tan (x)/*log\1 + x /*tan(x) + -----------------|
|| 2 | 2 2 2 |
|\ 1 + x / 1 + x / 2\ 1 + x |
\ \1 + x / /
$$\left(x^{2} + 1\right)^{\tan{\left(x \right)}} \left(- \frac{4 x^{2} \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{4 x \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 1} + \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)}\right)^{2} + 2 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)} \tan{\left(x \right)} + \frac{2 \tan{\left(x \right)}}{x^{2} + 1}\right)$$
tan(x) / 3 2 / 2 \ / 2 / 2 \\ 2 / 2 \ 3 / 2 \ \
/ 2\ |// 2 \ / 2\ 2*x*tan(x)\ / 2 \ / 2\ 6*\1 + tan (x)/ // 2 \ / 2\ 2*x*tan(x)\ |tan(x) / 2 \ / 2\ 2*x *tan(x) 2*x*\1 + tan (x)/| 12*x*tan(x) 12*x *\1 + tan (x)/ 2 / 2 \ / 2\ 16*x *tan(x) 12*x*\1 + tan (x)/*tan(x)|
\1 + x / *||\1 + tan (x)/*log\1 + x / + ----------| + 2*\1 + tan (x)/ *log\1 + x / + --------------- + 6*|\1 + tan (x)/*log\1 + x / + ----------|*|------ + \1 + tan (x)/*log\1 + x /*tan(x) - ----------- + -----------------| - ----------- - ------------------- + 4*tan (x)*\1 + tan (x)/*log\1 + x / + ------------ + -------------------------|
|| 2 | 2 | 2 | | 2 2 2 | 2 2 3 2 |
|\ 1 + x / 1 + x \ 1 + x / |1 + x / 2\ 1 + x | / 2\ / 2\ / 2\ 1 + x |
\ \ \1 + x / / \1 + x / \1 + x / \1 + x / /
$$\left(x^{2} + 1\right)^{\tan{\left(x \right)}} \left(\frac{16 x^{3} \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{3}} - \frac{12 x^{2} \left(\tan^{2}{\left(x \right)} + 1\right)}{\left(x^{2} + 1\right)^{2}} + \frac{12 x \left(\tan^{2}{\left(x \right)} + 1\right) \tan{\left(x \right)}}{x^{2} + 1} - \frac{12 x \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)}\right)^{3} + 6 \left(\frac{2 x \tan{\left(x \right)}}{x^{2} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)}\right) \left(- \frac{2 x^{2} \tan{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{2 x \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 1} + \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)} \tan{\left(x \right)} + \frac{\tan{\left(x \right)}}{x^{2} + 1}\right) + 2 \left(\tan^{2}{\left(x \right)} + 1\right)^{2} \log{\left(x^{2} + 1 \right)} + 4 \left(\tan^{2}{\left(x \right)} + 1\right) \log{\left(x^{2} + 1 \right)} \tan^{2}{\left(x \right)} + \frac{6 \left(\tan^{2}{\left(x \right)} + 1\right)}{x^{2} + 1}\right)$$