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(arcsin(x^2+3))^2

Derivative of (arcsin(x^2+3))^2

Function f() - derivative -N order at the point
v

The graph:

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The solution

You have entered [src]
    2/ 2    \
asin \x  + 3/
$$\operatorname{asin}^{2}{\left(x^{2} + 3 \right)}$$
d /    2/ 2    \\
--\asin \x  + 3//
dx               
$$\frac{d}{d x} \operatorname{asin}^{2}{\left(x^{2} + 3 \right)}$$
The graph
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 / /       /
$$8 x \left(\frac{6 x^{2} \left(x^{2} + 3\right)}{\left(\left(x^{2} + 3\right)^{2} - 1\right)^{2}} + \frac{2 x^{2} \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{3}{2}}} + \frac{6 x^{2} \left(x^{2} + 3\right)^{2} \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{5}{2}}} - \frac{3}{\left(x^{2} + 3\right)^{2} - 1} + \frac{3 \left(x^{2} + 3\right) \operatorname{asin}{\left(x^{2} + 3 \right)}}{\left(1 - \left(x^{2} + 3\right)^{2}\right)^{\frac{3}{2}}}\right)$$
The graph
Derivative of (arcsin(x^2+3))^2