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:
/ asin(x)\ / asin(x) asin(x) \
\E / |e e *log(x)|
x *|-------- + ---------------|
| x ________ |
| / 2 |
\ \/ 1 - x /
$$x^{e^{\operatorname{asin}{\left(x \right)}}} \left(\frac{e^{\operatorname{asin}{\left(x \right)}} \log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{e^{\operatorname{asin}{\left(x \right)}}}{x}\right)$$
/ asin(x)\ / 2 \
\e / | 1 /1 log(x) \ asin(x) log(x) 2 x*log(x) | asin(x)
x *|- -- + |- + -----------| *e - ------- + ------------- + -----------|*e
| 2 |x ________| 2 ________ 3/2|
| x | / 2 | -1 + x / 2 / 2\ |
\ \ \/ 1 - x / x*\/ 1 - x \1 - x / /
$$x^{e^{\operatorname{asin}{\left(x \right)}}} \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{1}{x}\right)^{2} e^{\operatorname{asin}{\left(x \right)}} - \frac{\log{\left(x \right)}}{x^{2} - 1} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{1}{x^{2}}\right) e^{\operatorname{asin}{\left(x \right)}}$$
/ asin(x)\ / 3 2 \
\e / |2 3 /1 log(x) \ 2*asin(x) 3 3 2*log(x) 3*x*log(x) 3*x *log(x) /1 log(x) \ / 1 log(x) 2 x*log(x) \ asin(x)| asin(x)
x *|-- + ----------- + |- + -----------| *e - ----------- - -------------- + ----------- + ---------- + ----------- + 3*|- + -----------|*|- -- - ------- + ------------- + -----------|*e |*e
| 3 3/2 |x ________| / 2\ ________ 3/2 2 5/2 |x ________| | 2 2 ________ 3/2| |
|x / 2\ | / 2 | x*\-1 + x / 2 / 2 / 2\ / 2\ / 2\ | / 2 | | x -1 + x / 2 / 2\ | |
\ \1 - x / \ \/ 1 - x / x *\/ 1 - x \1 - x / \-1 + x / \1 - x / \ \/ 1 - x / \ x*\/ 1 - x \1 - x / / /
$$x^{e^{\operatorname{asin}{\left(x \right)}}} \left(\frac{3 x^{2} \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} + \frac{3 x \log{\left(x \right)}}{\left(x^{2} - 1\right)^{2}} + \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{1}{x}\right)^{3} e^{2 \operatorname{asin}{\left(x \right)}} + 3 \left(\frac{\log{\left(x \right)}}{\sqrt{1 - x^{2}}} + \frac{1}{x}\right) \left(\frac{x \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{\log{\left(x \right)}}{x^{2} - 1} + \frac{2}{x \sqrt{1 - x^{2}}} - \frac{1}{x^{2}}\right) e^{\operatorname{asin}{\left(x \right)}} + \frac{2 \log{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{3}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \frac{3}{x \left(x^{2} - 1\right)} - \frac{3}{x^{2} \sqrt{1 - x^{2}}} + \frac{2}{x^{3}}\right) e^{\operatorname{asin}{\left(x \right)}}$$