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3x^2*arcsin(2x-1)

Derivative of 3x^2*arcsin(2x-1)

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

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The solution

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   2              
3*x *asin(2*x - 1)
$$3 x^{2} \operatorname{asin}{\left(2 x - 1 \right)}$$
d /   2              \
--\3*x *asin(2*x - 1)/
dx                    
$$\frac{d}{d x} 3 x^{2} \operatorname{asin}{\left(2 x - 1 \right)}$$
The graph
The first derivative [src]
                               2       
                            6*x        
6*x*asin(2*x - 1) + -------------------
                       ________________
                      /              2 
                    \/  1 - (2*x - 1)  
$$\frac{6 x^{2}}{\sqrt{1 - \left(2 x - 1\right)^{2}}} + 6 x \operatorname{asin}{\left(2 x - 1 \right)}$$
The second derivative [src]
  /                            2                               \
  |        4*x              2*x *(-1 + 2*x)                    |
6*|-------------------- + -------------------- + asin(-1 + 2*x)|
  |   _________________                    3/2                 |
  |  /               2    /              2\                    |
  \\/  1 - (-1 + 2*x)     \1 - (-1 + 2*x) /                    /
$$6 \cdot \left(\frac{2 x^{2} \cdot \left(2 x - 1\right)}{\left(1 - \left(2 x - 1\right)^{2}\right)^{\frac{3}{2}}} + \frac{4 x}{\sqrt{1 - \left(2 x - 1\right)^{2}}} + \operatorname{asin}{\left(2 x - 1 \right)}\right)$$
The third derivative [src]
   /         /                  2  \                  \
   |       2 |      3*(-1 + 2*x)   |                  |
   |    2*x *|-1 + ----------------|                  |
   |         |                    2|                  |
   |         \     -1 + (-1 + 2*x) /    6*x*(-1 + 2*x)|
12*|3 - ---------------------------- + ---------------|
   |                        2                        2|
   \          1 - (-1 + 2*x)           1 - (-1 + 2*x) /
-------------------------------------------------------
                     _________________                 
                    /               2                  
                  \/  1 - (-1 + 2*x)                   
$$\frac{12 \left(- \frac{2 x^{2} \cdot \left(\frac{3 \left(2 x - 1\right)^{2}}{\left(2 x - 1\right)^{2} - 1} - 1\right)}{1 - \left(2 x - 1\right)^{2}} + \frac{6 x \left(2 x - 1\right)}{1 - \left(2 x - 1\right)^{2}} + 3\right)}{\sqrt{1 - \left(2 x - 1\right)^{2}}}$$
The graph
Derivative of 3x^2*arcsin(2x-1)