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How to use it?
- Derivative of:
-
Derivative of 5x
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Derivative of 5x^3
- Derivative of 2*x-1
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Derivative of (2x+1)^2
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Identical expressions
- arcsin(two x/(one +x^2))
- arc sinus of (2x divide by (1 plus x squared ))
- arc sinus of (two x divide by (one plus x squared ))
- arcsin(2x/(1+x2))
- arcsin2x/1+x2
- arcsin(2x/(1+x²))
- arcsin(2x/(1+x to the power of 2))
- arcsin2x/1+x^2
- arcsin(2x divide by (1+x^2))
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Similar expressions
- arcsin(2x/(1-x^2))
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What you mean?
- asin(2*x/(1 + x^2))
- asin(2*x*2/(1 + x))
- asin(2*x/((1 + x)^2))
- asin(2*x/1 + x^2)
- asin(2*x/(1 + x^2))
- asin(2*x*2/(1 + x))
- asin(2*x/1 + x^2)
You entered:
arcsin(2x/(1+x^2))
What you mean?
Derivative of arcsin(2x/(1+x^2))
The solution
You have entered
[src]
/ 2*x \
asin|------|
| 2|
\1 + x /
$$\operatorname{asin}{\left(\frac{2 x}{x^{2} + 1} \right)}$$
d / / 2*x \\ --|asin|------|| dx| | 2|| \ \1 + x //
$$\frac{d}{d x} \operatorname{asin}{\left(\frac{2 x}{x^{2} + 1} \right)}$$
The first derivative
[src]
2
2 4*x
------ - ---------
2 2
1 + x / 2\
\1 + x /
----------------------
_______________
/ 2
/ 4*x
/ 1 - ---------
/ 2
/ / 2\
\/ \1 + x /
$$\frac{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + \frac{2}{x^{2} + 1}}{\sqrt{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1}}$$
The second derivative
[src]
/ 2 \
| / 2 \ |
| | 2*x | |
| 2*|-1 + ------| |
| 2 | 2| |
| 4*x \ 1 + x / |
4*x*|-3 + ------ + ------------------------|
| 2 / 2 \|
| 1 + x / 2\ | 4*x ||
| \1 + x /*|1 - ---------||
| | 2||
| | / 2\ ||
\ \ \1 + x / //
--------------------------------------------
_______________
2 / 2
/ 2\ / 4*x
\1 + x / * / 1 - ---------
/ 2
/ / 2\
\/ \1 + x /
$$\frac{4 x \left(\frac{4 x^{2}}{x^{2} + 1} - 3 + \frac{2 \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)^{2}}{\left(x^{2} + 1\right) \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)}\right)}{\left(x^{2} + 1\right)^{2} \sqrt{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1}}$$
The third derivative
[src]
/ / 2 \ / 2 4 \ 3 \
| | 2*x | | 10*x 12*x | / 2 \ / 2 \ / 2 \|
| 2*|-1 + ------|*|1 - ------ + ---------| 2 | 2*x | 2 | 2*x | | 4*x ||
| | 2| | 2 2| 24*x *|-1 + ------| 8*x *|-1 + ------|*|-3 + ------||
| 2 4 \ 1 + x / | 1 + x / 2\ | | 2| | 2| | 2||
| 24*x 24*x \ \1 + x / / \ 1 + x / \ 1 + x / \ 1 + x /|
-4*|3 - ------ + --------- + ---------------------------------------- + -------------------------- + --------------------------------|
| 2 2 / 2 \ 2 2 / 2 \ |
| 1 + x / 2\ / 2\ | 4*x | 3 / 2 \ / 2\ | 4*x | |
| \1 + x / \1 + x /*|1 - ---------| / 2\ | 4*x | \1 + x / *|1 - ---------| |
| | 2| \1 + x / *|1 - ---------| | 2| |
| | / 2\ | | 2| | / 2\ | |
| \ \1 + x / / | / 2\ | \ \1 + x / / |
\ \ \1 + x / / /
--------------------------------------------------------------------------------------------------------------------------------------
_______________
2 / 2
/ 2\ / 4*x
\1 + x / * / 1 - ---------
/ 2
/ / 2\
\/ \1 + x /
$$- \frac{4 \cdot \left(\frac{24 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{24 x^{2}}{x^{2} + 1} + \frac{8 x^{2} \cdot \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \left(\frac{4 x^{2}}{x^{2} + 1} - 3\right)}{\left(x^{2} + 1\right)^{2} \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)} + \frac{24 x^{2} \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right)^{3}}{\left(x^{2} + 1\right)^{3} \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)^{2}} + 3 + \frac{2 \cdot \left(\frac{2 x^{2}}{x^{2} + 1} - 1\right) \left(\frac{12 x^{4}}{\left(x^{2} + 1\right)^{2}} - \frac{10 x^{2}}{x^{2} + 1} + 1\right)}{\left(x^{2} + 1\right) \left(- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1\right)}\right)}{\left(x^{2} + 1\right)^{2} \sqrt{- \frac{4 x^{2}}{\left(x^{2} + 1\right)^{2}} + 1}}$$
The graph