Mister Exam
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- Derivative of a implicit defined function
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How to use it?
- Derivative of:
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Derivative of (-2)/x^3
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Derivative of e^(x*(-4))
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Derivative of y=(x^4)÷2
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Derivative of y=1/cos²x
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Identical expressions
- arcsin((2x- one)/sqrt(three))
- arc sinus of ((2x minus 1) divide by square root of (3))
- arc sinus of ((2x minus one) divide by square root of (three))
- arcsin((2x-1)/√(3))
- arcsin2x-1/sqrt3
- arcsin((2x-1) divide by sqrt(3))
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Similar expressions
- (arcsin(2x-1)/(sqrt3))
- arcsin((2x+1)/sqrt(3))
Derivative of arcsin((2x-1)/sqrt(3))
The solution
You have entered
[src]
/2*x - 1\
asin|-------|
| ___ |
\ \/ 3 /
$$\operatorname{asin}{\left(\frac{2 x - 1}{\sqrt{3}} \right)}$$
asin((2*x - 1)/sqrt(3))
The first derivative
[src]
___
2*\/ 3
-----------------------
________________
/ 2
/ (2*x - 1)
3* / 1 - ----------
\/ 3
$$\frac{2 \sqrt{3}}{3 \sqrt{1 - \frac{\left(2 x - 1\right)^{2}}{3}}}$$
The second derivative
[src]
___
4*\/ 3 *(-1 + 2*x)
----------------------
3/2
/ 2\
| (-1 + 2*x) |
9*|1 - -----------|
\ 3 /
$$\frac{4 \sqrt{3} \left(2 x - 1\right)}{9 \left(1 - \frac{\left(2 x - 1\right)^{2}}{3}\right)^{\frac{3}{2}}}$$
The third derivative
[src]
/ 2 \
___ | (-1 + 2*x) |
8*\/ 3 *|1 + ---------------|
| 2|
| (-1 + 2*x) |
| 1 - -----------|
\ 3 /
-----------------------------
3/2
/ 2\
| (-1 + 2*x) |
9*|1 - -----------|
\ 3 /
$$\frac{8 \sqrt{3} \left(1 + \frac{\left(2 x - 1\right)^{2}}{1 - \frac{\left(2 x - 1\right)^{2}}{3}}\right)}{9 \left(1 - \frac{\left(2 x - 1\right)^{2}}{3}\right)^{\frac{3}{2}}}$$