The first derivative
[src]
/ 2 \
4*x*asin\x + 3/
-------------------
_______________
/ 2
/ / 2 \
\/ 1 - \x + 3/
$$\frac{4 x \operatorname{asin}{\left(x^{2} + 3 \right)}}{\sqrt{1 - \left(x^{2} + 3\right)^{2}}}$$
The second derivative
[src]
/ / 2\ 2 2 / 2\ / 2\\
| asin\3 + x / 2*x 2*x *\3 + x /*asin\3 + x /|
4*|------------------- - -------------- + --------------------------|
| _______________ 2 3/2 |
| / 2 / 2\ / 2\ |
| / / 2\ -1 + \3 + x / | / 2\ | |
\\/ 1 - \3 + x / \1 - \3 + x / / /
$$4 \left(- \frac{2 x^{2}}{\left(x^{2} + 3\right)^{2} - 1} + \frac{2 x^{2} \left(x^{2} + 3\right) \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{3}{2}}} + \frac{\operatorname{asin}{\left(x^{2} + 3 \right)}}{\sqrt{1 - \left(x^{2} + 3\right)^{2}}}\right)$$
The third derivative
[src]
/ 2 \
| 2 / 2\ / 2\ / 2\ 2 / 2\ 2 / 2\ / 2\|
| 3 2*x *asin\3 + x / 3*\3 + x /*asin\3 + x / 6*x *\3 + x / 6*x *\3 + x / *asin\3 + x /|
8*x*|- -------------- + ------------------ + ----------------------- + ----------------- + ---------------------------|
| 2 3/2 3/2 2 5/2 |
| / 2\ / 2\ / 2\ / 2\ / 2\ |
| -1 + \3 + x / | / 2\ | | / 2\ | | / 2\ | | / 2\ | |
\ \1 - \3 + x / / \1 - \3 + x / / \-1 + \3 + x / / \1 - \3 + x / / /
$$8 x \left(\frac{6 x^{2} \left(x^{2} + 3\right)}{\left(\left(x^{2} + 3\right)^{2} - 1\right)^{2}} + \frac{2 x^{2} \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{3}{2}}} + \frac{6 x^{2} \left(x^{2} + 3\right)^{2} \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{5}{2}}} - \frac{3}{\left(x^{2} + 3\right)^{2} - 1} + \frac{3 \left(x^{2} + 3\right) \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{3}{2}}}\right)$$