Solución detallada
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No logro encontrar los pasos en la búsqueda de esta derivada.
Perola derivada
Respuesta:
x
2 / 2*x / 2 \\
asin (x) *|------------------- + log\asin (x)/|
| ________ |
| / 2 |
\\/ 1 - x *asin(x) /
$$\left(\frac{2 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \log{\left(\operatorname{asin}^{2}{\left(x \right)} \right)}\right) \left(\operatorname{asin}^{2}{\left(x \right)}\right)^{x}$$
/ / 2 \\
| | 2 x x ||
| 2*|----------- + ----------- + -----------------||
| | ________ 3/2 / 2\ ||
x | 2 | / 2 / 2\ \-1 + x /*asin(x)||
2 |/ 2*x / 2 \\ \\/ 1 - x \1 - x / /|
asin (x) *||------------------- + log\asin (x)/| + -------------------------------------------------|
|| ________ | asin(x) |
|| / 2 | |
\\\/ 1 - x *asin(x) / /
$$\left(\left(\frac{2 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \log{\left(\operatorname{asin}^{2}{\left(x \right)} \right)}\right)^{2} + \frac{2 \left(\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \frac{2}{\sqrt{1 - x^{2}}}\right)}{\operatorname{asin}{\left(x \right)}}\right) \left(\operatorname{asin}^{2}{\left(x \right)}\right)^{x}$$
/ / 3 2 \ / 2 \\
| | 3*x 3 4*x 3*x 2*x | / 2*x / 2 \\ | 2 x x ||
| 2*|----------- + ----------------- + ----------- - ------------------ + --------------------| 6*|------------------- + log\asin (x)/|*|----------- + ----------- + -----------------||
| | 5/2 / 2\ 3/2 2 3/2 | | ________ | | ________ 3/2 / 2\ ||
x | 3 |/ 2\ \-1 + x /*asin(x) / 2\ / 2\ / 2\ 2 | | / 2 | | / 2 / 2\ \-1 + x /*asin(x)||
2 |/ 2*x / 2 \\ \\1 - x / \1 - x / \-1 + x / *asin(x) \1 - x / *asin (x)/ \\/ 1 - x *asin(x) / \\/ 1 - x \1 - x / /|
asin (x) *||------------------- + log\asin (x)/| + --------------------------------------------------------------------------------------------- + ---------------------------------------------------------------------------------------|
|| ________ | asin(x) asin(x) |
|| / 2 | |
\\\/ 1 - x *asin(x) / /
$$\left(\left(\frac{2 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \log{\left(\operatorname{asin}^{2}{\left(x \right)} \right)}\right)^{3} + \frac{6 \left(\frac{2 x}{\sqrt{1 - x^{2}} \operatorname{asin}{\left(x \right)}} + \log{\left(\operatorname{asin}^{2}{\left(x \right)} \right)}\right) \left(\frac{x^{2}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{x}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}} + \frac{2}{\sqrt{1 - x^{2}}}\right)}{\operatorname{asin}{\left(x \right)}} + \frac{2 \left(\frac{3 x^{3}}{\left(1 - x^{2}\right)^{\frac{5}{2}}} - \frac{3 x^{2}}{\left(x^{2} - 1\right)^{2} \operatorname{asin}{\left(x \right)}} + \frac{4 x}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \frac{2 x}{\left(1 - x^{2}\right)^{\frac{3}{2}} \operatorname{asin}^{2}{\left(x \right)}} + \frac{3}{\left(x^{2} - 1\right) \operatorname{asin}{\left(x \right)}}\right)}{\operatorname{asin}{\left(x \right)}}\right) \left(\operatorname{asin}^{2}{\left(x \right)}\right)^{x}$$