Mister Exam
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How to use it?
- Derivative of:
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Derivative of 1/2sin2x
- Derivative of ln(4x+3)
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Derivative of csc7x
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Derivative of arcsin(x/(sqrt(1-x^2)))
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Identical expressions
- arcsin(x/(sqrt(one -x^ two)))
- arc sinus of (x divide by ( square root of (1 minus x squared )))
- arc sinus of (x divide by ( square root of (one minus x to the power of two)))
- arcsin(x/(√(1-x^2)))
- arcsin(x/(sqrt(1-x2)))
- arcsinx/sqrt1-x2
- arcsin(x/(sqrt(1-x²)))
- arcsin(x/(sqrt(1-x to the power of 2)))
- arcsinx/sqrt1-x^2
- arcsin(x divide by (sqrt(1-x^2)))
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Similar expressions
- arcsin(x/(sqrt(1+x^2)))
Derivative of arcsin(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 | | x ||
| |1 + ------|*|-1 + -------||
| 2 | 2| | 2||
| 1 2 3*x \ 1 - x / \ -1 + x /|
x*|- ------- + ------ + --------- + ---------------------------|
| 2 2 2 / 2 \ |
| -1 + x 1 - x / 2\ | x | / 2\ |
| \1 - x / |1 - ------|*\-1 + x / |
| | 2| |
\ \ 1 - x / /
----------------------------------------------------------------
____________
________ / 2
/ 2 / x
\/ 1 - x * / 1 - ------
/ 2
\/ 1 - x
$$\frac{x \left(\frac{3 x^{2}}{\left(- x^{2} + 1\right)^{2}} + \frac{\left(\frac{x^{2}}{- x^{2} + 1} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)}{\left(x^{2} - 1\right) \left(- \frac{x^{2}}{- x^{2} + 1} + 1\right)} - \frac{1}{x^{2} - 1} + \frac{2}{- x^{2} + 1}\right)}{\sqrt{- x^{2} + 1} \sqrt{- \frac{x^{2}}{- x^{2} + 1} + 1}}$$
The third derivative
[src]
/ 4 2 \ / 2 \ / 2 4 \ / 2 \ / 2 \ 2
| 5*x 6*x | | x | | 5*x 4*x | 2 | x | | 1 2 3*x | / 2 \ / 2 \
3*|1 + --------- + ------| |1 + ------|*|1 - ------- + ----------| 2*x *|-1 + -------|*|- ------- + ------ + ---------| 2 | x | | x |
| 2 2| | 2| | 2 2| | 2| | 2 2 2| 3*x *|-1 + -------| *|1 + ------|
| / 2\ 1 - x | \ 1 - x / | -1 + x / 2\ | \ -1 + x / | -1 + x 1 - x / 2\ | | 2| | 2|
\ \1 - x / / \ \-1 + x / / \ \1 - x / / \ -1 + x / \ 1 - x /
-------------------------- - --------------------------------------- + ---------------------------------------------------- + ---------------------------------
2 / 2 \ / 2 \ 2
1 - x | x | / 2\ | x | / 2\ / 2 \ 2
|1 - ------|*\-1 + x / |1 - ------|*\-1 + x / | x | / 2\
| 2| | 2| |1 - ------| *\-1 + x /
\ 1 - x / \ 1 - x / | 2|
\ 1 - x /
---------------------------------------------------------------------------------------------------------------------------------------------------------------
____________
________ / 2
/ 2 / x
\/ 1 - x * / 1 - ------
/ 2
\/ 1 - x
$$\frac{\frac{2 x^{2} \left(\frac{x^{2}}{x^{2} - 1} - 1\right) \left(\frac{3 x^{2}}{\left(- x^{2} + 1\right)^{2}} - \frac{1}{x^{2} - 1} + \frac{2}{- x^{2} + 1}\right)}{\left(x^{2} - 1\right) \left(- \frac{x^{2}}{- x^{2} + 1} + 1\right)} + \frac{3 x^{2} \left(\frac{x^{2}}{- x^{2} + 1} + 1\right) \left(\frac{x^{2}}{x^{2} - 1} - 1\right)^{2}}{\left(x^{2} - 1\right)^{2} \left(- \frac{x^{2}}{- x^{2} + 1} + 1\right)^{2}} - \frac{\left(\frac{x^{2}}{- x^{2} + 1} + 1\right) \left(\frac{4 x^{4}}{\left(x^{2} - 1\right)^{2}} - \frac{5 x^{2}}{x^{2} - 1} + 1\right)}{\left(x^{2} - 1\right) \left(- \frac{x^{2}}{- x^{2} + 1} + 1\right)} + \frac{3 \cdot \left(\frac{5 x^{4}}{\left(- x^{2} + 1\right)^{2}} + \frac{6 x^{2}}{- x^{2} + 1} + 1\right)}{- x^{2} + 1}}{\sqrt{- x^{2} + 1} \sqrt{- \frac{x^{2}}{- x^{2} + 1} + 1}}$$
The graph