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