Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ / 2 \ \
| |1 + --|*sin(x)|
sin(x) | | 3| |
/ 1 \ | / 1 \ \ x / |
|x - --| *|cos(x)*log|x - --| + ---------------|
| 2| | | 2| 1 |
\ x / | \ x / x - -- |
| 2 |
\ x /
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}} \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right)$$
/ 2 2 \
|/ / 2 \ \ / 2 \ / 2 \ |
|| |1 + --|*sin(x)| |1 + --| *sin(x) 2*|1 + --|*cos(x)|
sin(x) || | 3| | | 3| | 3| |
/ 1 \ || / 1 \ \ x / | / 1 \ \ x / 6*sin(x) \ x / |
|x - --| *||cos(x)*log|x - --| + ---------------| - log|x - --|*sin(x) - ---------------- - ----------- + -----------------|
| 2| || | 2| 1 | | 2| 2 4 / 1 \ 1 |
\ x / || \ x / x - -- | \ x / / 1 \ x *|x - --| x - -- |
|| 2 | |x - --| | 2| 2 |
|\ x / | 2| \ x / x |
\ \ x / /
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}} \left(- \frac{\left(1 + \frac{2}{x^{3}}\right)^{2} \sin{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{2}} + \frac{2 \left(1 + \frac{2}{x^{3}}\right) \cos{\left(x \right)}}{x - \frac{1}{x^{2}}} + \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right)^{2} - \log{\left(x - \frac{1}{x^{2}} \right)} \sin{\left(x \right)} - \frac{6 \sin{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)}\right)$$
/ 3 / 2 \ 2 3 \
|/ / 2 \ \ / / 2 \ \ | / 2 \ / 2 \ | / 2 \ / 2 \ / 2 \ / 2 \ |
|| |1 + --|*sin(x)| | |1 + --|*sin(x)| | |1 + --| *sin(x) 2*|1 + --|*cos(x) | 3*|1 + --| *cos(x) 3*|1 + --|*sin(x) 2*|1 + --| *sin(x) 18*|1 + --|*sin(x)|
sin(x) || | 3| | | | 3| | | | 3| | 3| | | 3| | 3| | 3| | 3| |
/ 1 \ || / 1 \ \ x / | / 1 \ | / 1 \ \ x / | | / 1 \ \ x / \ x / 6*sin(x) | 18*cos(x) \ x / \ x / \ x / 24*sin(x) \ x / |
|x - --| *||cos(x)*log|x - --| + ---------------| - cos(x)*log|x - --| - 3*|cos(x)*log|x - --| + ---------------|*|log|x - --|*sin(x) + ---------------- - ----------------- + -----------| - ----------- - ------------------ - ----------------- + ------------------ + ----------- + ------------------|
| 2| || | 2| 1 | | 2| | | 2| 1 | | | 2| 2 1 4 / 1 \| 4 / 1 \ 2 1 3 5 / 1 \ 2 |
\ x / || \ x / x - -- | \ x / | \ x / x - -- | | \ x / / 1 \ x - -- x *|x - --|| x *|x - --| / 1 \ x - -- / 1 \ x *|x - --| 4 / 1 \ |
|| 2 | | 2 | | |x - --| 2 | 2|| | 2| |x - --| 2 |x - --| | 2| x *|x - --| |
|\ x / \ x / | | 2| x \ x /| \ x / | 2| x | 2| \ x / | 2| |
\ \ \ x / / \ x / \ x / \ x / /
$$\left(x - \frac{1}{x^{2}}\right)^{\sin{\left(x \right)}} \left(\frac{2 \left(1 + \frac{2}{x^{3}}\right)^{3} \sin{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{3}} - \frac{3 \left(1 + \frac{2}{x^{3}}\right)^{2} \cos{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{2}} - \frac{3 \left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right)^{3} - 3 \left(\frac{\left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)}\right) \left(\frac{\left(1 + \frac{2}{x^{3}}\right)^{2} \sin{\left(x \right)}}{\left(x - \frac{1}{x^{2}}\right)^{2}} - \frac{2 \left(1 + \frac{2}{x^{3}}\right) \cos{\left(x \right)}}{x - \frac{1}{x^{2}}} + \log{\left(x - \frac{1}{x^{2}} \right)} \sin{\left(x \right)} + \frac{6 \sin{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)}\right) - \log{\left(x - \frac{1}{x^{2}} \right)} \cos{\left(x \right)} + \frac{18 \left(1 + \frac{2}{x^{3}}\right) \sin{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)^{2}} - \frac{18 \cos{\left(x \right)}}{x^{4} \left(x - \frac{1}{x^{2}}\right)} + \frac{24 \sin{\left(x \right)}}{x^{5} \left(x - \frac{1}{x^{2}}\right)}\right)$$