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