Mister Exam
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How to use it?
- Derivative of:
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Derivative of u
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Derivative of e^x/x^2
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Derivative of cos(x)/x^2
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Derivative of cos(sqrt(x))
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Identical expressions
- arccos((x- one)/(two -x))
- arc co sinus of e of ((x minus 1) divide by (2 minus x))
- arc co sinus of e of ((x minus one) divide by (two minus x))
- arccosx-1/2-x
- arccos((x-1) divide by (2-x))
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Similar expressions
- arccos((x+1)/(2-x))
- arccos((x-1)/(2+x))
Derivative of arccos((x-1)/(2-x))
The solution
You have entered
[src]
/x - 1\
acos|-----|
\2 - x/
$$\operatorname{acos}{\left(\frac{x - 1}{2 - x} \right)}$$
The first derivative
[src]
/ 1 x - 1 \
-|----- + --------|
|2 - x 2|
\ (2 - x) /
--------------------
______________
/ 2
/ (x - 1)
/ 1 - --------
/ 2
\/ (2 - x)
$$- \frac{\frac{1}{2 - x} + \frac{x - 1}{\left(2 - x\right)^{2}}}{\sqrt{1 - \frac{\left(x - 1\right)^{2}}{\left(2 - x\right)^{2}}}}$$
The second derivative
[src]
/ / -1 + x\ \
| |1 - ------|*(-1 + x) |
/ -1 + x\ | \ -2 + x/ |
|1 - ------|*|-2 + ------------------------|
\ -2 + x/ | / 2\ |
| | (-1 + x) | |
| |1 - ---------|*(-2 + x)|
| | 2| |
\ \ (-2 + x) / /
--------------------------------------------
_______________
/ 2
/ (-1 + x) 2
/ 1 - --------- *(-2 + x)
/ 2
\/ (-2 + x)
$$\frac{\left(-2 + \frac{\left(1 - \frac{x - 1}{x - 2}\right) \left(x - 1\right)}{\left(1 - \frac{\left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}\right) \left(x - 2\right)}\right) \left(1 - \frac{x - 1}{x - 2}\right)}{\sqrt{1 - \frac{\left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}} \left(x - 2\right)^{2}}$$
The third derivative
[src]
/ 2 \
| 4*(-1 + x) 3*(-1 + x) 2 |
| 1 - ---------- + ----------- / -1 + x\ / -1 + x\ 2 |
| -2 + x 2 4*|1 - ------|*(-1 + x) 3*|1 - ------| *(-1 + x) |
/ -1 + x\ | (-2 + x) \ -2 + x/ \ -2 + x/ |
|1 - ------|*|6 + ---------------------------- - ------------------------ + --------------------------|
\ -2 + x/ | 2 / 2\ 2 |
| (-1 + x) | (-1 + x) | / 2\ |
| 1 - --------- |1 - ---------|*(-2 + x) | (-1 + x) | 2|
| 2 | 2| |1 - ---------| *(-2 + x) |
| (-2 + x) \ (-2 + x) / | 2| |
\ \ (-2 + x) / /
-------------------------------------------------------------------------------------------------------
_______________
/ 2
/ (-1 + x) 3
/ 1 - --------- *(-2 + x)
/ 2
\/ (-2 + x)
$$\frac{\left(1 - \frac{x - 1}{x - 2}\right) \left(6 - \frac{4 \left(1 - \frac{x - 1}{x - 2}\right) \left(x - 1\right)}{\left(1 - \frac{\left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}\right) \left(x - 2\right)} + \frac{1 - \frac{4 \left(x - 1\right)}{x - 2} + \frac{3 \left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}}{1 - \frac{\left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}} + \frac{3 \left(1 - \frac{x - 1}{x - 2}\right)^{2} \left(x - 1\right)^{2}}{\left(1 - \frac{\left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}\right)^{2} \left(x - 2\right)^{2}}\right)}{\sqrt{1 - \frac{\left(x - 1\right)^{2}}{\left(x - 2\right)^{2}}} \left(x - 2\right)^{3}}$$
The graph