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The derivative of the function/ arcsin(1/x^3)

Derivative of arcsin(1/x^3)

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

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The solution

You have entered [src] 
    /1 \
asin|--|
    | 3|
    \x /
$$\operatorname{asin}{\left(\frac{1}{x^{3}} \right)}$$ 
asin(1/(x^3))
The graph
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      -3        
----------------
        ________
 4     /     1  
x *   /  1 - -- 
     /        6 
   \/        x
$$- \frac{3}{x^{4} \sqrt{1 - \frac{1}{x^{6}}}}$$
Simplify
The second derivative [src] 
  /         3     \
3*|4 + -----------|
  |     6 /    1 \|
  |    x *|1 - --||
  |       |     6||
  \       \    x //
-------------------
          ________ 
   5     /     1   
  x *   /  1 - --  
       /        6  
     \/        x
$$\frac{3 \left(4 + \frac{3}{x^{6} \left(1 - \frac{1}{x^{6}}\right)}\right)}{x^{5} \sqrt{1 - \frac{1}{x^{6}}}}$$
Simplify
The third derivative [src] 
   /           27             45    \
-3*|20 + ------------- + -----------|
   |                 2    6 /    1 \|
   |      12 /    1 \    x *|1 - --||
   |     x  *|1 - --|       |     6||
   |         |     6|       \    x /|
   \         \    x /               /
-------------------------------------
                   ________          
            6     /     1            
           x *   /  1 - --           
                /        6           
              \/        x
$$- \frac{3 \left(20 + \frac{45}{x^{6} \left(1 - \frac{1}{x^{6}}\right)} + \frac{27}{x^{12} \left(1 - \frac{1}{x^{6}}\right)^{2}}\right)}{x^{6} \sqrt{1 - \frac{1}{x^{6}}}}$$
Simplify
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