Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
sin(2*x) / sin(x)*sin(2*x)\
cos (x)*|2*cos(2*x)*log(cos(x)) - ---------------|
\ cos(x) /
$$\left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) \cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$
/ 2 2 \
sin(2*x) |/ sin(x)*sin(2*x)\ sin (x)*sin(2*x) 4*cos(2*x)*sin(x)|
cos (x)*||2*cos(2*x)*log(cos(x)) - ---------------| - sin(2*x) - 4*log(cos(x))*sin(2*x) - ---------------- - -----------------|
|\ cos(x) / 2 cos(x) |
\ cos (x) /
$$\left(\left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)^{2} - 4 \log{\left(\cos{\left(x \right)} \right)} \sin{\left(2 x \right)} - \frac{\sin^{2}{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(x \right)}} - \frac{4 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\cos{\left(x \right)}} - \sin{\left(2 x \right)}\right) \cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$
/ 3 / 2 \ 2 3 \
sin(2*x) |/ sin(x)*sin(2*x)\ / sin(x)*sin(2*x)\ | sin (x)*sin(2*x) 4*cos(2*x)*sin(x) | 6*sin (x)*cos(2*x) 2*sin (x)*sin(2*x) 10*sin(x)*sin(2*x)|
cos (x)*||2*cos(2*x)*log(cos(x)) - ---------------| - 6*cos(2*x) - 8*cos(2*x)*log(cos(x)) - 3*|2*cos(2*x)*log(cos(x)) - ---------------|*|4*log(cos(x))*sin(2*x) + ---------------- + ----------------- + sin(2*x)| - ------------------ - ------------------ + ------------------|
|\ cos(x) / \ cos(x) / | 2 cos(x) | 2 3 cos(x) |
\ \ cos (x) / cos (x) cos (x) /
$$\left(\left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right)^{3} - 3 \left(2 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{\sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}}\right) \left(4 \log{\left(\cos{\left(x \right)} \right)} \sin{\left(2 x \right)} + \frac{\sin^{2}{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{2}{\left(x \right)}} + \frac{4 \sin{\left(x \right)} \cos{\left(2 x \right)}}{\cos{\left(x \right)}} + \sin{\left(2 x \right)}\right) - 8 \log{\left(\cos{\left(x \right)} \right)} \cos{\left(2 x \right)} - \frac{2 \sin^{3}{\left(x \right)} \sin{\left(2 x \right)}}{\cos^{3}{\left(x \right)}} - \frac{6 \sin^{2}{\left(x \right)} \cos{\left(2 x \right)}}{\cos^{2}{\left(x \right)}} + \frac{10 \sin{\left(x \right)} \sin{\left(2 x \right)}}{\cos{\left(x \right)}} - 6 \cos{\left(2 x \right)}\right) \cos^{\sin{\left(2 x \right)}}{\left(x \right)}$$