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