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The derivative of the function/ arccos(x/a)

Derivative of arccos(x/a)

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

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from to

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The solution

You have entered [src] 
    /x\
acos|-|
    \a/
$$\operatorname{acos}{\left(\frac{x}{a} \right)}$$ 
acos(x/a)
The first derivative [src] 
      -1        
----------------
        ________
       /      2 
      /      x  
a*   /   1 - -- 
    /         2 
  \/         a
$$- \frac{1}{a \sqrt{1 - \frac{x^{2}}{a^{2}}}}$$
Simplify
The second derivative [src] 
     -x       
--------------
           3/2
   /     2\   
 3 |    x |   
a *|1 - --|   
   |     2|   
   \    a /
$$- \frac{x}{a^{3} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}}$$
Simplify
The third derivative [src] 
 /           2   \ 
 |        3*x    | 
-|1 + -----------| 
 |       /     2\| 
 |     2 |    x || 
 |    a *|1 - --|| 
 |       |     2|| 
 \       \    a // 
-------------------
              3/2  
      /     2\     
    3 |    x |     
   a *|1 - --|     
      |     2|     
      \    a /
$$- \frac{1 + \frac{3 x^{2}}{a^{2} \left(1 - \frac{x^{2}}{a^{2}}\right)}}{a^{3} \left(1 - \frac{x^{2}}{a^{2}}\right)^{\frac{3}{2}}}$$
Simplify
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