Mister Exam
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How to use it?
- Derivative of:
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Derivative of (-2)/x^2
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Derivative of (cos(x))^sin(x)
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Derivative of y=(x+2)²(2x-1)³
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Derivative of y=5x-6
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Identical expressions
- -arcsin((lnx)/(sqrt(two)))+c
- minus arc sinus of ((lnx) divide by ( square root of (2))) plus c
- minus arc sinus of ((lnx) divide by ( square root of (two))) plus c
- -arcsin((lnx)/(√(2)))+c
- -arcsinlnx/sqrt2+c
- -arcsin((lnx) divide by (sqrt(2)))+c
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Similar expressions
- arcsin((lnx)/(sqrt(2)))+c
- -arcsin((lnx)/(sqrt(2)))-c
Derivative of -arcsin((lnx)/(sqrt(2)))+c
The solution
You have entered
[src]
/log(x)\
- asin|------| + c
| ___ |
\\/ 2 /
$$c - \operatorname{asin}{\left(\frac{\log{\left(x \right)}}{\sqrt{2}} \right)}$$
d / /log(x)\ \ --|- asin|------| + c| dx| | ___ | | \ \\/ 2 / /
$$\frac{\partial}{\partial x} \left(c - \operatorname{asin}{\left(\frac{\log{\left(x \right)}}{\sqrt{2}} \right)}\right)$$
The first derivative
[src]
___
-\/ 2
----------------------
_____________
/ 2
/ log (x)
2*x* / 1 - -------
\/ 2
$$- \frac{\sqrt{2}}{2 x \sqrt{- \frac{\log{\left(x \right)}^{2}}{2} + 1}}$$
The second derivative
[src]
___ / log(x) \
\/ 2 *|2 - -----------|
| 2 |
| log (x)|
| 1 - -------|
\ 2 /
-----------------------
_____________
/ 2
2 / log (x)
4*x * / 1 - -------
\/ 2
$$\frac{\sqrt{2} \cdot \left(2 - \frac{\log{\left(x \right)}}{- \frac{\log{\left(x \right)}^{2}}{2} + 1}\right)}{4 x^{2} \sqrt{- \frac{\log{\left(x \right)}^{2}}{2} + 1}}$$
The third derivative
[src]
/ 2 \
___ | 1 3*log (x) 3*log(x) |
\/ 2 *|-1 - --------------- - ---------------- + ---------------|
| / 2 \ 2 / 2 \|
| | log (x)| / 2 \ | log (x)||
| 4*|1 - -------| | log (x)| 4*|1 - -------||
| \ 2 / 8*|1 - -------| \ 2 /|
\ \ 2 / /
-----------------------------------------------------------------
_____________
/ 2
3 / log (x)
x * / 1 - -------
\/ 2
$$\frac{\sqrt{2} \left(-1 + \frac{3 \log{\left(x \right)}}{4 \cdot \left(- \frac{\log{\left(x \right)}^{2}}{2} + 1\right)} - \frac{3 \log{\left(x \right)}^{2}}{8 \left(- \frac{\log{\left(x \right)}^{2}}{2} + 1\right)^{2}} - \frac{1}{4 \cdot \left(- \frac{\log{\left(x \right)}^{2}}{2} + 1\right)}\right)}{x^{3} \sqrt{- \frac{\log{\left(x \right)}^{2}}{2} + 1}}$$