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