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How to use it?
- Derivative of:
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Derivative of 8^x
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Derivative of 2*sinh(x)*cosh(x)
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Derivative of x^2*asinh(x)*acosh(x)
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Derivative of (x^2-4)/x
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Identical expressions
- (arcsin(x^ two + three))^ two
- (arc sinus of (x squared plus 3)) squared
- (arc sinus of (x to the power of two plus three)) to the power of two
- (arcsin(x2+3))2
- arcsinx2+32
- (arcsin(x²+3))²
- (arcsin(x to the power of 2+3)) to the power of 2
- arcsinx^2+3^2
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Similar expressions
- (arcsin(x^2-3))^2
Derivative of (arcsin(x^2+3))^2
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 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