Solución detallada
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Perola derivada
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Simplificamos:
Respuesta:
/ 2*x\
\E / / / ___\ 2*x \
/ / ___\\ | 2*x / / ___\\ cos\\/ x /*e |
\sin\\/ x // *|2*e *log\sin\\/ x // + ------------------|
| ___ / ___\|
\ 2*\/ x *sin\\/ x //
$$\left(2 e^{2 x} \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{e^{2 x} \cos{\left(\sqrt{x} \right)}}{2 \sqrt{x} \sin{\left(\sqrt{x} \right)}}\right) \sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$
/ 2 \
| / / ___\ \ |
| | / / ___\\ cos\\/ x / | 2*x |
/ 2*x\ | |4*log\sin\\/ x // + ----------------| *e |
\e / | | ___ / ___\| / ___\ 2/ ___\ / ___\ |
/ / ___\\ | / / ___\\ 1 \ \/ x *sin\\/ x // 2*cos\\/ x / cos \\/ x / cos\\/ x / | 2*x
\sin\\/ x // *|4*log\sin\\/ x // - --- + -------------------------------------------- + ---------------- - --------------- - -----------------|*e
| 4*x 4 ___ / ___\ 2/ ___\ 3/2 / ___\|
\ \/ x *sin\\/ x / 4*x*sin \\/ x / 4*x *sin\\/ x //
$$\left(\frac{\left(4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right)^{2} e^{2 x}}{4} + 4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} - \frac{1}{4 x} - \frac{\cos^{2}{\left(\sqrt{x} \right)}}{4 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{2 \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} - \frac{\cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) e^{2 x} \sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$
/ 3 \
| / / ___\ \ / / ___\ \ / 2/ ___\ / ___\ / ___\ \ |
| | / / ___\\ cos\\/ x / | 4*x | / / ___\\ cos\\/ x / | |1 / / ___\\ cos \\/ x / cos\\/ x / 8*cos\\/ x / | 2*x |
/ 2*x\ | |4*log\sin\\/ x // + ----------------| *e 3*|4*log\sin\\/ x // + ----------------|*|- - 16*log\sin\\/ x // + ------------- + --------------- - ----------------|*e |
\e / | | ___ / ___\| / ___\ / ___\ 2/ ___\ | ___ / ___\| |x 2/ ___\ 3/2 / ___\ ___ / ___\| 3/ ___\ 2/ ___\ / ___\ |
/ / ___\\ | / / ___\\ 3 3 \ \/ x *sin\\/ x // 6*cos\\/ x / 5*cos\\/ x / 3*cos \\/ x / \ \/ x *sin\\/ x // \ x*sin \\/ x / x *sin\\/ x / \/ x *sin\\/ x // cos \\/ x / 3*cos \\/ x / 3*cos\\/ x / | 2*x
\sin\\/ x // *|8*log\sin\\/ x // - --- + ---- + -------------------------------------------- + ---------------- - ----------------- - --------------- - --------------------------------------------------------------------------------------------------------------------------- + ------------------ + ---------------- + -----------------|*e
| 2*x 2 8 ___ / ___\ 3/2 / ___\ 2/ ___\ 8 3/2 3/ ___\ 2 2/ ___\ 5/2 / ___\|
\ 8*x \/ x *sin\\/ x / 4*x *sin\\/ x / 2*x*sin \\/ x / 4*x *sin \\/ x / 8*x *sin \\/ x / 8*x *sin\\/ x //
$$\left(\frac{\left(4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right)^{3} e^{4 x}}{8} - \frac{3 \left(4 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{\cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}}\right) \left(- 16 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} + \frac{1}{x} + \frac{\cos^{2}{\left(\sqrt{x} \right)}}{x \sin^{2}{\left(\sqrt{x} \right)}} - \frac{8 \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} + \frac{\cos{\left(\sqrt{x} \right)}}{x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}}\right) e^{2 x}}{8} + 8 \log{\left(\sin{\left(\sqrt{x} \right)} \right)} - \frac{3}{2 x} - \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{2 x \sin^{2}{\left(\sqrt{x} \right)}} + \frac{3}{8 x^{2}} + \frac{3 \cos^{2}{\left(\sqrt{x} \right)}}{8 x^{2} \sin^{2}{\left(\sqrt{x} \right)}} + \frac{6 \cos{\left(\sqrt{x} \right)}}{\sqrt{x} \sin{\left(\sqrt{x} \right)}} - \frac{5 \cos{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin{\left(\sqrt{x} \right)}} + \frac{\cos^{3}{\left(\sqrt{x} \right)}}{4 x^{\frac{3}{2}} \sin^{3}{\left(\sqrt{x} \right)}} + \frac{3 \cos{\left(\sqrt{x} \right)}}{8 x^{\frac{5}{2}} \sin{\left(\sqrt{x} \right)}}\right) e^{2 x} \sin^{e^{2 x}}{\left(\sqrt{x} \right)}$$