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