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The derivative of the function/ arccos*(3/x)

Derivative of arccos*(3/x)

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] 
    /3\
acos|-|
    \x/
$$\operatorname{acos}{\left(\frac{3}{x} \right)}$$ 
acos(3/x)
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
       3        
----------------
        ________
 2     /     9  
x *   /  1 - -- 
     /        2 
   \/        x
$$\frac{3}{x^{2} \sqrt{1 - \frac{9}{x^{2}}}}$$
Simplify
The second derivative [src] 
   /         9     \
-3*|2 + -----------|
   |     2 /    9 \|
   |    x *|1 - --||
   |       |     2||
   \       \    x //
--------------------
          ________  
   3     /     9    
  x *   /  1 - --   
       /        2   
     \/        x
$$- \frac{3 \left(2 + \frac{9}{x^{2} \left(1 - \frac{9}{x^{2}}\right)}\right)}{x^{3} \sqrt{1 - \frac{9}{x^{2}}}}$$
Simplify
The third derivative [src] 
  /         21            81     \
9*|2 + ----------- + ------------|
  |     2 /    9 \              2|
  |    x *|1 - --|    4 /    9 \ |
  |       |     2|   x *|1 - --| |
  |       \    x /      |     2| |
  \                     \    x / /
----------------------------------
                 ________         
          4     /     9           
         x *   /  1 - --          
              /        2          
            \/        x
$$\frac{9 \left(2 + \frac{21}{x^{2} \left(1 - \frac{9}{x^{2}}\right)} + \frac{81}{x^{4} \left(1 - \frac{9}{x^{2}}\right)^{2}}\right)}{x^{4} \sqrt{1 - \frac{9}{x^{2}}}}$$
Simplify
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