Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
x - 2
----- / / 2 \ \
3 |log(cot(x)) \-1 - cot (x)/*(x - 2)|
(cot(x)) *|----------- + ----------------------|
\ 3 3*cot(x) /
$$\left(\frac{\left(x - 2\right) \left(- \cot^{2}{\left(x \right)} - 1\right)}{3 \cot{\left(x \right)}} + \frac{\log{\left(\cot{\left(x \right)} \right)}}{3}\right) \cot^{\frac{x - 2}{3}}{\left(x \right)}$$
2 x / 2 \
- - + - |/ / 2 \ \ / / 2 \ \|
3 3 || \1 + cot (x)/*(-2 + x)| / 2 \ | 2 \1 + cot (x)/*(-2 + x)||
(cot(x)) *||-log(cot(x)) + ----------------------| - 3*\1 + cot (x)/*|4 - 2*x + ------ + ----------------------||
|\ cot(x) / | cot(x) 2 ||
\ \ cot (x) //
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9
$$\frac{\left(\left(\frac{\left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right)^{2} - 3 \left(\cot^{2}{\left(x \right)} + 1\right) \left(- 2 x + \frac{\left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} + 4 + \frac{2}{\cot{\left(x \right)}}\right)\right) \cot^{\frac{x}{3} - \frac{2}{3}}{\left(x \right)}}{9}$$
/ 3 / / 2 \ \ / / 2 \ \ \
| / / 2 \ \ / 2 \ | \1 + cot (x)/*(-2 + x)| | 2 \1 + cot (x)/*(-2 + x)| |
2 x | | \1 + cot (x)/*(-2 + x)| 2 3 \1 + cot (x)/*|-log(cot(x)) + ----------------------|*|4 - 2*x + ------ + ----------------------| 2 |
- - + - | |-log(cot(x)) + ----------------------| / 2 \ / 2 \ / 2 \ \ cot(x) / | cot(x) 2 | / 2 \ |
3 3 | 2 \ cot(x) / \1 + cot (x)/ 4*\1 + cot (x)/*(-2 + x)*cot(x) 2*\1 + cot (x)/ *(-2 + x) \ cot (x) / 4*\1 + cot (x)/ *(-2 + x)|
(cot(x)) *|2 + 2*cot (x) - ---------------------------------------- - -------------- - ------------------------------- - ------------------------- + ------------------------------------------------------------------------------------------------- + -------------------------|
| 27 2 3 3 3 3*cot(x) |
\ cot (x) 3*cot (x) /
$$\left(- \frac{2 \left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{3}}{3 \cot^{3}{\left(x \right)}} + \frac{4 \left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{3 \cot{\left(x \right)}} - \frac{4 \left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right) \cot{\left(x \right)}}{3} - \frac{\left(\frac{\left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right)^{3}}{27} + \frac{\left(\frac{\left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot{\left(x \right)}} - \log{\left(\cot{\left(x \right)} \right)}\right) \left(\cot^{2}{\left(x \right)} + 1\right) \left(- 2 x + \frac{\left(x - 2\right) \left(\cot^{2}{\left(x \right)} + 1\right)}{\cot^{2}{\left(x \right)}} + 4 + \frac{2}{\cot{\left(x \right)}}\right)}{3} - \frac{\left(\cot^{2}{\left(x \right)} + 1\right)^{2}}{\cot^{2}{\left(x \right)}} + 2 \cot^{2}{\left(x \right)} + 2\right) \cot^{\frac{x}{3} - \frac{2}{3}}{\left(x \right)}$$