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How to use it?
- Derivative of:
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Derivative of asin(x/sqrt(1+x^2))
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Derivative of cos(3x+5)
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Derivative of 6t^2
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Derivative of sin^4x+cos^4x
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Identical expressions
- asin(x/sqrt(one +x^ two))
- arc sinus of e of (x divide by square root of (1 plus x squared ))
- arc sinus of e of (x divide by square root of (one plus x to the power of two))
- asin(x/√(1+x^2))
- asin(x/sqrt(1+x2))
- asinx/sqrt1+x2
- asin(x/sqrt(1+x²))
- asin(x/sqrt(1+x to the power of 2))
- asinx/sqrt1+x^2
- asin(x divide by sqrt(1+x^2))
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Similar expressions
- asin(x/sqrt(1-x^2))
- arcsin(x/sqrt(1+x^2))
Derivative of asin(x/sqrt(1+x^2))
The solution
You have entered
[src]
/ x \
asin|-----------|
| ________|
| / 2 |
\\/ 1 + x /
$$\operatorname{asin}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}$$
d / / x \\ --|asin|-----------|| dx| | ________|| | | / 2 || \ \\/ 1 + x //
$$\frac{d}{d x} \operatorname{asin}{\left(\frac{x}{\sqrt{x^{2} + 1}} \right)}$$
The first derivative
[src]
2
1 x
----------- - -----------
________ 3/2
/ 2 / 2\
\/ 1 + x \1 + x /
-------------------------
____________
/ 2
/ x
/ 1 - ------
/ 2
\/ 1 + x
$$\frac{- \frac{x^{2}}{\left(x^{2} + 1\right)^{\frac{3}{2}}} + \frac{1}{\sqrt{x^{2} + 1}}}{\sqrt{- \frac{x^{2}}{x^{2} + 1} + 1}}$$
The second derivative
[src]
/ 2\
| / 2 \ |
| | x | |
| ____________ |-1 + ------| |
| / 2 | 2| |
| / x \ 1 + x / |
x*|- 3* / 1 - ------ + ---------------|
| / 2 3/2|
| \/ 1 + x / 2 \ |
| | x | |
| |1 - ------| |
| | 2| |
\ \ 1 + x / /
--------------------------------------------
3/2
/ 2\
\1 + x /
$$\frac{x \left(- 3 \sqrt{- \frac{x^{2}}{x^{2} + 1} + 1} + \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right)^{2}}{\left(- \frac{x^{2}}{x^{2} + 1} + 1\right)^{\frac{3}{2}}}\right)}{\left(x^{2} + 1\right)^{\frac{3}{2}}}$$
The third derivative
[src]
/ 2 \ / 2 4 \ 3
| x | | 5*x 4*x | / 2 \ / 2 \
|-1 + ------|*|1 - ------ + ---------| 2 | x | 2 | x |
| 2| | 2 2| 6*x *|-1 + ------| 3*x *|-1 + ------|
4 2 \ 1 + x / | 1 + x / 2\ | | 2| | 2|
15*x 18*x \ \1 + x / / \ 1 + x / \ 1 + x /
-3 - --------- + ------ - -------------------------------------- + ------------------ - ----------------------
2 2 2 2 2
/ 2\ 1 + x x 1 + x / 2 \
\1 + x / 1 - ------ / 2\ | x |
2 \1 + x /*|1 - ------|
1 + x | 2|
\ 1 + x /
--------------------------------------------------------------------------------------------------------------
____________
3/2 / 2
/ 2\ / x
\1 + x / * / 1 - ------
/ 2
\/ 1 + x
$$\frac{- \frac{15 x^{4}}{\left(x^{2} + 1\right)^{2}} + \frac{6 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)}{x^{2} + 1} - \frac{3 x^{2} \left(\frac{x^{2}}{x^{2} + 1} - 1\right)^{3}}{\left(x^{2} + 1\right) \left(- \frac{x^{2}}{x^{2} + 1} + 1\right)^{2}} + \frac{18 x^{2}}{x^{2} + 1} - \frac{\left(\frac{x^{2}}{x^{2} + 1} - 1\right) \left(\frac{4 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{5 x^{2}}{x^{2} + 1} + 1\right)}{- \frac{x^{2}}{x^{2} + 1} + 1} - 3}{\left(x^{2} + 1\right)^{\frac{3}{2}} \sqrt{- \frac{x^{2}}{x^{2} + 1} + 1}}$$
The graph