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(x)\ / sin(x) \
\E / |e sin(x) |
x *|------- + cos(x)*e *log(x)|
\ x /
$$x^{e^{\sin{\left(x \right)}}} \left(e^{\sin{\left(x \right)}} \log{\left(x \right)} \cos{\left(x \right)} + \frac{e^{\sin{\left(x \right)}}}{x}\right)$$
/ sin(x)\ / 2 \
\e / | 1 /1 \ sin(x) 2 2*cos(x)| sin(x)
x *|- -- + |- + cos(x)*log(x)| *e + cos (x)*log(x) - log(x)*sin(x) + --------|*e
| 2 \x / x |
\ x /
$$x^{e^{\sin{\left(x \right)}}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{1}{x}\right)^{2} e^{\sin{\left(x \right)}} - \log{\left(x \right)} \sin{\left(x \right)} + \log{\left(x \right)} \cos^{2}{\left(x \right)} + \frac{2 \cos{\left(x \right)}}{x} - \frac{1}{x^{2}}\right) e^{\sin{\left(x \right)}}$$
/ sin(x)\ / 3 2 \
\e / |2 /1 \ 2*sin(x) 3 3*sin(x) 3*cos(x) 3*cos (x) /1 \ /1 2 2*cos(x)\ sin(x) | sin(x)
x *|-- + |- + cos(x)*log(x)| *e + cos (x)*log(x) - cos(x)*log(x) - -------- - -------- + --------- - 3*|- + cos(x)*log(x)|*|-- + log(x)*sin(x) - cos (x)*log(x) - --------|*e - 3*cos(x)*log(x)*sin(x)|*e
| 3 \x / x 2 x \x / | 2 x | |
\x x \x / /
$$x^{e^{\sin{\left(x \right)}}} \left(\left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{1}{x}\right)^{3} e^{2 \sin{\left(x \right)}} - 3 \left(\log{\left(x \right)} \cos{\left(x \right)} + \frac{1}{x}\right) \left(\log{\left(x \right)} \sin{\left(x \right)} - \log{\left(x \right)} \cos^{2}{\left(x \right)} - \frac{2 \cos{\left(x \right)}}{x} + \frac{1}{x^{2}}\right) e^{\sin{\left(x \right)}} - 3 \log{\left(x \right)} \sin{\left(x \right)} \cos{\left(x \right)} + \log{\left(x \right)} \cos^{3}{\left(x \right)} - \log{\left(x \right)} \cos{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x} + \frac{3 \cos^{2}{\left(x \right)}}{x} - \frac{3 \cos{\left(x \right)}}{x^{2}} + \frac{2}{x^{3}}\right) e^{\sin{\left(x \right)}}$$