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