Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
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Simplificamos:
Respuesta:
2*x + 1 / 3*(2*x + 1)*sin(3*x)\
cos (3*x)*|2*log(cos(3*x)) - --------------------|
\ cos(3*x) /
$$\left(- \frac{3 \left(2 x + 1\right) \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} + 2 \log{\left(\cos{\left(3 x \right)} \right)}\right) \cos^{2 x + 1}{\left(3 x \right)}$$
/ 2 2 \
1 + 2*x | / 3*(1 + 2*x)*sin(3*x)\ 12*sin(3*x) 9*sin (3*x)*(1 + 2*x)|
cos (3*x)*|-9 + |-2*log(cos(3*x)) + --------------------| - 18*x - ----------- - ---------------------|
| \ cos(3*x) / cos(3*x) 2 |
\ cos (3*x) /
$$\left(- 18 x - \frac{9 \left(2 x + 1\right) \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + \left(\frac{3 \left(2 x + 1\right) \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - 2 \log{\left(\cos{\left(3 x \right)} \right)}\right)^{2} - \frac{12 \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - 9\right) \cos^{2 x + 1}{\left(3 x \right)}$$
/ 3 2 / 2 \ 3 \
1 + 2*x | / 3*(1 + 2*x)*sin(3*x)\ 54*sin (3*x) / 3*(1 + 2*x)*sin(3*x)\ | 4*sin(3*x) 3*sin (3*x)*(1 + 2*x)| 54*(1 + 2*x)*sin(3*x) 54*sin (3*x)*(1 + 2*x)|
cos (3*x)*|-54 - |-2*log(cos(3*x)) + --------------------| - ------------ + 9*|-2*log(cos(3*x)) + --------------------|*|3 + 6*x + ---------- + ---------------------| - --------------------- - ----------------------|
| \ cos(3*x) / 2 \ cos(3*x) / | cos(3*x) 2 | cos(3*x) 3 |
\ cos (3*x) \ cos (3*x) / cos (3*x) /
$$\left(- \frac{54 \left(2 x + 1\right) \sin^{3}{\left(3 x \right)}}{\cos^{3}{\left(3 x \right)}} - \frac{54 \left(2 x + 1\right) \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - \left(\frac{3 \left(2 x + 1\right) \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - 2 \log{\left(\cos{\left(3 x \right)} \right)}\right)^{3} + 9 \left(\frac{3 \left(2 x + 1\right) \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} - 2 \log{\left(\cos{\left(3 x \right)} \right)}\right) \left(6 x + \frac{3 \left(2 x + 1\right) \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} + \frac{4 \sin{\left(3 x \right)}}{\cos{\left(3 x \right)}} + 3\right) - \frac{54 \sin^{2}{\left(3 x \right)}}{\cos^{2}{\left(3 x \right)}} - 54\right) \cos^{2 x + 1}{\left(3 x \right)}$$