Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ 2\ / 2 / 2 \\
\x / | x *\-3 - 3*cot (3*x)/|
(cot(3*x)) *|2*x*log(cot(3*x)) + ---------------------|
\ cot(3*x) /
$$\left(\frac{x^{2} \left(- 3 \cot^{2}{\left(3 x \right)} - 3\right)}{\cot{\left(3 x \right)}} + 2 x \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{x^{2}}{\left(3 x \right)}$$
/ 2 2\
/ 2\ | / / 2 \\ / 2 \ 2 / 2 \ |
\x / | 2 | 3*x*\1 + cot (3*x)/| 2 / 2 \ 12*x*\1 + cot (3*x)/ 9*x *\1 + cot (3*x)/ |
(cot(3*x)) *|2*log(cot(3*x)) + x *|-2*log(cot(3*x)) + -------------------| + 18*x *\1 + cot (3*x)/ - -------------------- - ---------------------|
| \ cot(3*x) / cot(3*x) 2 |
\ cot (3*x) /
$$\left(x^{2} \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right)^{2} - \frac{9 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} + 18 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right) - \frac{12 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) \cot^{x^{2}}{\left(3 x \right)}$$
/ 3 / 2\ / 2 \\
/ 2\ | / / 2 \\ | 2 / 2 \ / 2 \ 2 / 2 \ | / / 2 \\ | 2 / 2 \ / 2 \||
\x / | 3 | 3*x*\1 + cot (3*x)/| / 2 \ | 1 2 6*x *\1 + cot (3*x)/ 3*x*\1 + cot (3*x)/ 3*x *\1 + cot (3*x)/ | | 3*x*\1 + cot (3*x)/| | 2 / 2 \ 9*x *\1 + cot (3*x)/ 12*x*\1 + cot (3*x)/||
(cot(3*x)) *|- x *|-2*log(cot(3*x)) + -------------------| - 18*\1 + cot (3*x)/*|-------- - 6*x + 6*x *cot(3*x) - -------------------- + ------------------- + ---------------------| + 3*x*|-2*log(cot(3*x)) + -------------------|*|-2*log(cot(3*x)) - 18*x *\1 + cot (3*x)/ + --------------------- + --------------------||
| \ cot(3*x) / |cot(3*x) cot(3*x) 2 3 | \ cot(3*x) / | 2 cot(3*x) ||
\ \ cot (3*x) cot (3*x) / \ cot (3*x) //
$$\left(- x^{3} \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right)^{3} + 3 x \left(\frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) \left(\frac{9 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{2}{\left(3 x \right)}} - 18 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right) + \frac{12 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} - 2 \log{\left(\cot{\left(3 x \right)} \right)}\right) - 18 \left(\cot^{2}{\left(3 x \right)} + 1\right) \left(\frac{3 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)^{2}}{\cot^{3}{\left(3 x \right)}} - \frac{6 x^{2} \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot{\left(3 x \right)}} + 6 x^{2} \cot{\left(3 x \right)} + \frac{3 x \left(\cot^{2}{\left(3 x \right)} + 1\right)}{\cot^{2}{\left(3 x \right)}} - 6 x + \frac{1}{\cot{\left(3 x \right)}}\right)\right) \cot^{x^{2}}{\left(3 x \right)}$$