Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
cos(5*x)
/ 2 \ / / 2 \ 2*x*cos(5*x)\
\x + 1/ *|- 5*log\x + 1/*sin(5*x) + ------------|
| 2 |
\ x + 1 /
$$\left(x^{2} + 1\right)^{\cos{\left(5 x \right)}} \left(\frac{2 x \cos{\left(5 x \right)}}{x^{2} + 1} - 5 \log{\left(x^{2} + 1 \right)} \sin{\left(5 x \right)}\right)$$
cos(5*x) / 2 2 \
/ 2\ |/ / 2\ 2*x*cos(5*x)\ / 2\ 2*cos(5*x) 20*x*sin(5*x) 4*x *cos(5*x)|
\1 + x / *||- 5*log\1 + x /*sin(5*x) + ------------| - 25*cos(5*x)*log\1 + x / + ---------- - ------------- - -------------|
|| 2 | 2 2 2 |
|\ 1 + x / 1 + x 1 + x / 2\ |
\ \1 + x / /
$$\left(x^{2} + 1\right)^{\cos{\left(5 x \right)}} \left(- \frac{4 x^{2} \cos{\left(5 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{20 x \sin{\left(5 x \right)}}{x^{2} + 1} + \left(\frac{2 x \cos{\left(5 x \right)}}{x^{2} + 1} - 5 \log{\left(x^{2} + 1 \right)} \sin{\left(5 x \right)}\right)^{2} - 25 \log{\left(x^{2} + 1 \right)} \cos{\left(5 x \right)} + \frac{2 \cos{\left(5 x \right)}}{x^{2} + 1}\right)$$
cos(5*x) / 3 / 2 \ 3 2 \
/ 2\ |/ / 2\ 2*x*cos(5*x)\ 30*sin(5*x) / / 2\ 2*x*cos(5*x)\ | 2*cos(5*x) / 2\ 4*x *cos(5*x) 20*x*sin(5*x)| / 2\ 150*x*cos(5*x) 12*x*cos(5*x) 16*x *cos(5*x) 60*x *sin(5*x)|
\1 + x / *||- 5*log\1 + x /*sin(5*x) + ------------| - ----------- - 3*|- 5*log\1 + x /*sin(5*x) + ------------|*|- ---------- + 25*cos(5*x)*log\1 + x / + ------------- + -------------| + 125*log\1 + x /*sin(5*x) - -------------- - ------------- + -------------- + --------------|
|| 2 | 2 | 2 | | 2 2 2 | 2 2 3 2 |
|\ 1 + x / 1 + x \ 1 + x / | 1 + x / 2\ 1 + x | 1 + x / 2\ / 2\ / 2\ |
\ \ \1 + x / / \1 + x / \1 + x / \1 + x / /
$$\left(x^{2} + 1\right)^{\cos{\left(5 x \right)}} \left(\frac{16 x^{3} \cos{\left(5 x \right)}}{\left(x^{2} + 1\right)^{3}} + \frac{60 x^{2} \sin{\left(5 x \right)}}{\left(x^{2} + 1\right)^{2}} - \frac{150 x \cos{\left(5 x \right)}}{x^{2} + 1} - \frac{12 x \cos{\left(5 x \right)}}{\left(x^{2} + 1\right)^{2}} + \left(\frac{2 x \cos{\left(5 x \right)}}{x^{2} + 1} - 5 \log{\left(x^{2} + 1 \right)} \sin{\left(5 x \right)}\right)^{3} - 3 \left(\frac{2 x \cos{\left(5 x \right)}}{x^{2} + 1} - 5 \log{\left(x^{2} + 1 \right)} \sin{\left(5 x \right)}\right) \left(\frac{4 x^{2} \cos{\left(5 x \right)}}{\left(x^{2} + 1\right)^{2}} + \frac{20 x \sin{\left(5 x \right)}}{x^{2} + 1} + 25 \log{\left(x^{2} + 1 \right)} \cos{\left(5 x \right)} - \frac{2 \cos{\left(5 x \right)}}{x^{2} + 1}\right) + 125 \log{\left(x^{2} + 1 \right)} \sin{\left(5 x \right)} - \frac{30 \sin{\left(5 x \right)}}{x^{2} + 1}\right)$$