Mister Exam

Other calculators

arccos((x-1)/(2-x))
The derivative of the function/ arccos((x-1)/(2-x))

Derivative of arccos((x-1)/(2-x))

Function f() - derivative -N order at the point
v

The graph:

from to

Piecewise:

The solution

You have entered [src] 
    /x - 1\
acos|-----|
    \2 - x/
acos⁡(x−12−x)\operatorname{acos}{\left(\frac{x - 1}{2 - x} \right)}
Transform
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
 /  1      x - 1  \ 
-|----- + --------| 
 |2 - x          2| 
 \        (2 - x) / 
--------------------
      ______________
     /            2 
    /      (x - 1)  
   /   1 - -------- 
  /               2 
\/         (2 - x)
−12−x+x−1(2−x)21−(x−1)2(2−x)2- \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}}}}
Simplify
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)
(−2+(1−x−1x−2)(x−1)(1−(x−1)2(x−2)2)(x−2))(1−x−1x−2)1−(x−1)2(x−2)2(x−2)2\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}}
Simplify
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)
(1−x−1x−2)(6−4(1−x−1x−2)(x−1)(1−(x−1)2(x−2)2)(x−2)+1−4(x−1)x−2+3(x−1)2(x−2)21−(x−1)2(x−2)2+3(1−x−1x−2)2(x−1)2(1−(x−1)2(x−2)2)2(x−2)2)1−(x−1)2(x−2)2(x−2)3\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}}
Simplify
The graph
Derivative of arccos((x-1)/(2-x))
    © Mister Exam – Calculator