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The derivative of the function/ (asin(2x)^3)

Derivative of (asin(2x)^3)

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

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The solution

You have entered [src] 
    3     
asin (2*x)
$$\operatorname{asin}^{3}{\left(2 x \right)}$$ 
asin(2*x)^3
The graph
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The first derivative [src] 
       2     
 6*asin (2*x)
-------------
   __________
  /        2 
\/  1 - 4*x
$$\frac{6 \operatorname{asin}^{2}{\left(2 x \right)}}{\sqrt{1 - 4 x^{2}}}$$
Simplify
The second derivative [src] 
   /      1        x*asin(2*x) \          
24*|- --------- + -------------|*asin(2*x)
   |          2             3/2|          
   |  -1 + 4*x    /       2\   |          
   \              \1 - 4*x /   /
$$24 \left(\frac{x \operatorname{asin}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} - \frac{1}{4 x^{2} - 1}\right) \operatorname{asin}{\left(2 x \right)}$$
Simplify
The third derivative [src] 
   /                      2                              2     2     \
   |      2           asin (2*x)    12*x*asin(2*x)   12*x *asin (2*x)|
24*|------------- + ------------- + -------------- + ----------------|
   |          3/2             3/2               2               5/2  |
   |/       2\      /       2\       /        2\      /       2\     |
   \\1 - 4*x /      \1 - 4*x /       \-1 + 4*x /      \1 - 4*x /     /
$$24 \left(\frac{12 x^{2} \operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{5}{2}}} + \frac{12 x \operatorname{asin}{\left(2 x \right)}}{\left(4 x^{2} - 1\right)^{2}} + \frac{\operatorname{asin}^{2}{\left(2 x \right)}}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}} + \frac{2}{\left(1 - 4 x^{2}\right)^{\frac{3}{2}}}\right)$$
Simplify
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