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:
sin(3*x)
--------
2 /sin(3*x) 3*cos(3*x)*log(x)\
x *|-------- + -----------------|
\ 2*x 2 /
$$x^{\frac{\sin{\left(3 x \right)}}{2}} \left(\frac{3 \log{\left(x \right)} \cos{\left(3 x \right)}}{2} + \frac{\sin{\left(3 x \right)}}{2 x}\right)$$
/ 2 \
sin(3*x) |/sin(3*x) \ |
-------- ||-------- + 3*cos(3*x)*log(x)| |
2 |\ x / 3*cos(3*x) 9*log(x)*sin(3*x) sin(3*x)|
x *|------------------------------- + ---------- - ----------------- - --------|
| 4 x 2 2 |
\ 2*x /
$$x^{\frac{\sin{\left(3 x \right)}}{2}} \left(\frac{\left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)^{2}}{4} - \frac{9 \log{\left(x \right)} \sin{\left(3 x \right)}}{2} + \frac{3 \cos{\left(3 x \right)}}{x} - \frac{\sin{\left(3 x \right)}}{2 x^{2}}\right)$$
/ 3 /sin(3*x) \ /sin(3*x) 6*cos(3*x) \\
sin(3*x) |/sin(3*x) \ 3*|-------- + 3*cos(3*x)*log(x)|*|-------- - ---------- + 9*log(x)*sin(3*x)||
-------- ||-------- + 3*cos(3*x)*log(x)| \ x / | 2 x ||
2 |\ x / sin(3*x) 27*sin(3*x) 27*cos(3*x)*log(x) 9*cos(3*x) \ x /|
x *|------------------------------- + -------- - ----------- - ------------------ - ---------- - ----------------------------------------------------------------------------|
| 8 3 2*x 2 2 4 |
\ x 2*x /
$$x^{\frac{\sin{\left(3 x \right)}}{2}} \left(\frac{\left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right)^{3}}{8} - \frac{3 \left(3 \log{\left(x \right)} \cos{\left(3 x \right)} + \frac{\sin{\left(3 x \right)}}{x}\right) \left(9 \log{\left(x \right)} \sin{\left(3 x \right)} - \frac{6 \cos{\left(3 x \right)}}{x} + \frac{\sin{\left(3 x \right)}}{x^{2}}\right)}{4} - \frac{27 \log{\left(x \right)} \cos{\left(3 x \right)}}{2} - \frac{27 \sin{\left(3 x \right)}}{2 x} - \frac{9 \cos{\left(3 x \right)}}{2 x^{2}} + \frac{\sin{\left(3 x \right)}}{x^{3}}\right)$$