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