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arcosin(cos(x/3))
The derivative of the function/ arcosin(cos(x/3))

Derivative of arcosin(cos(x/3))

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

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The solution

You have entered [src] 
    /   /x\\
acos|cos|-||
    \   \3//
acos⁡(cos⁡(x3))\operatorname{acos}{\left(\cos{\left(\frac{x}{3} \right)} \right)} 
acos(cos(x/3))
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
          /x\      
       sin|-|      
          \3/      
-------------------
      _____________
     /        2/x\ 
3*  /  1 - cos |-| 
  \/           \3/
sin⁡(x3)31−cos⁡2(x3)\frac{\sin{\left(\frac{x}{3} \right)}}{3 \sqrt{1 - \cos^{2}{\left(\frac{x}{3} \right)}}}
Simplify
The second derivative [src] 
/         2/x\  \       
|      sin |-|  |       
|          \3/  |    /x\
|1 - -----------|*cos|-|
|           2/x\|    \3/
|    1 - cos |-||       
\            \3//       
------------------------
        _____________   
       /        2/x\    
  9*  /  1 - cos |-|    
    \/           \3/
(1−sin⁡2(x3)1−cos⁡2(x3))cos⁡(x3)91−cos⁡2(x3)\frac{\left(1 - \frac{\sin^{2}{\left(\frac{x}{3} \right)}}{1 - \cos^{2}{\left(\frac{x}{3} \right)}}\right) \cos{\left(\frac{x}{3} \right)}}{9 \sqrt{1 - \cos^{2}{\left(\frac{x}{3} \right)}}}
Simplify
The third derivative [src] 
/          2/x\           2/x\         2/x\    2/x\\       
|       sin |-|      3*cos |-|    3*cos |-|*sin |-||       
|           \3/            \3/          \3/     \3/|    /x\
|-1 + ----------- - ----------- + -----------------|*sin|-|
|            2/x\          2/x\                  2 |    \3/
|     1 - cos |-|   1 - cos |-|     /       2/x\\  |       
|             \3/           \3/     |1 - cos |-||  |       
\                                   \        \3//  /       
-----------------------------------------------------------
                           _____________                   
                          /        2/x\                    
                    27*  /  1 - cos |-|                    
                       \/           \3/
(−1+sin⁡2(x3)1−cos⁡2(x3)−3cos⁡2(x3)1−cos⁡2(x3)+3sin⁡2(x3)cos⁡2(x3)(1−cos⁡2(x3))2)sin⁡(x3)271−cos⁡2(x3)\frac{\left(-1 + \frac{\sin^{2}{\left(\frac{x}{3} \right)}}{1 - \cos^{2}{\left(\frac{x}{3} \right)}} - \frac{3 \cos^{2}{\left(\frac{x}{3} \right)}}{1 - \cos^{2}{\left(\frac{x}{3} \right)}} + \frac{3 \sin^{2}{\left(\frac{x}{3} \right)} \cos^{2}{\left(\frac{x}{3} \right)}}{\left(1 - \cos^{2}{\left(\frac{x}{3} \right)}\right)^{2}}\right) \sin{\left(\frac{x}{3} \right)}}{27 \sqrt{1 - \cos^{2}{\left(\frac{x}{3} \right)}}}
Simplify
The graph
Derivative of arcosin(cos(x/3))
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