Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
/ 4\ / 4 \
\x / | 3 x |
(asin(x)) *|4*x *log(asin(x)) + -------------------|
| ________ |
| / 2 |
\ \/ 1 - x *asin(x)/
$$\left(\frac{x^{4}}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 x^{3} \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \operatorname{asin}^{x^{4}}{\left(x \right)}$$
/ 4\ / 2 2 3 \
2 \x / | 4 / x \ x x 8*x |
x *(asin(x)) *|12*log(asin(x)) + x *|4*log(asin(x)) + -------------------| + ------------------ + ------------------- + -------------------|
| | ________ | / 2\ 2 3/2 ________ |
| | / 2 | \-1 + x /*asin (x) / 2\ / 2 |
\ \ \/ 1 - x *asin(x)/ \1 - x / *asin(x) \/ 1 - x *asin(x)/
$$x^{2} \left(x^{4} \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right)^{2} + \frac{x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{8 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 12 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \operatorname{asin}^{x^{4}}{\left(x \right)}$$
/ 4\ / 3 4 3 / 2 3 \ 5 2 3 \
\x / | 8 / x \ 3*x 2*x 4 / x \ | x x 8*x | 3*x 12*x 13*x 36*x |
x*(asin(x)) *|24*log(asin(x)) + x *|4*log(asin(x)) + -------------------| - ------------------- + -------------------- + 3*x *|4*log(asin(x)) + -------------------|*|12*log(asin(x)) + ------------------ + ------------------- + -------------------| + ------------------- + ------------------ + ------------------- + -------------------|
| | ________ | 2 3/2 | ________ | | / 2\ 2 3/2 ________ | 5/2 / 2\ 2 3/2 ________ |
| | / 2 | / 2\ 2 / 2\ 3 | / 2 | | \-1 + x /*asin (x) / 2\ / 2 | / 2\ \-1 + x /*asin (x) / 2\ / 2 |
\ \ \/ 1 - x *asin(x)/ \-1 + x / *asin (x) \1 - x / *asin (x) \ \/ 1 - x *asin(x)/ \ \1 - x / *asin(x) \/ 1 - x *asin(x)/ \1 - x / *asin(x) \1 - x / *asin(x) \/ 1 - x *asin(x)/
$$x \left(x^{8} \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right)^{3} + \frac{3 x^{5}}{\left(1 - x^{2}\right)^{\frac{5}{2}} \operatorname{asin}{\left(x \right)}} + 3 x^{4} \left(\frac{x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 4 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \left(\frac{x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{8 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 12 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) - \frac{3 x^{4}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}^{2}{\left(x \right)}} + \frac{13 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}{\left(x \right)}} + \frac{2 x^{3}}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{3}{\left(x \right)}} + \frac{12 x^{2}}{\left(x^{2} - 1\right) \operatorname{asin}^{2}{\left(x \right)}} + \frac{36 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + 24 \log{\left(\operatorname{asin}{\left(x \right)} \right)}\right) \operatorname{asin}^{x^{4}}{\left(x \right)}$$