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

Derivative of asin(x/3)*sin(2*x)

Function f() - derivative -N order at the point
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The solution

You have entered [src] 
    /x\         
asin|-|*sin(2*x)
    \3/
sin⁡(2x)asin⁡(x3)\sin{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} 
asin(x/3)*sin(2*x)
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
      /x\                sin(2*x)   
2*asin|-|*cos(2*x) + ---------------
      \3/                   ________
                           /      2 
                          /      x  
                     3*  /   1 - -- 
                       \/        9
2cos⁡(2x)asin⁡(x3)+sin⁡(2x)31−x292 \cos{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} + \frac{\sin{\left(2 x \right)}}{3 \sqrt{1 - \frac{x^{2}}{9}}}
Simplify
The second derivative [src] 
        /x\               4*cos(2*x)       x*sin(2*x)  
- 4*asin|-|*sin(2*x) + --------------- + --------------
        \3/                   ________              3/2
                             /      2       /     2\   
                            /      x        |    x |   
                       3*  /   1 - --    27*|1 - --|   
                         \/        9        \    9 /
xsin⁡(2x)27(1−x29)32−4sin⁡(2x)asin⁡(x3)+4cos⁡(2x)31−x29\frac{x \sin{\left(2 x \right)}}{27 \left(1 - \frac{x^{2}}{9}\right)^{\frac{3}{2}}} - 4 \sin{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} + \frac{4 \cos{\left(2 x \right)}}{3 \sqrt{1 - \frac{x^{2}}{9}}}
Simplify
The third derivative [src] 
                                       /          2 \                         
                                       |       3*x  |                         
                                       |-1 + -------|*sin(2*x)                
                                       |           2|                         
        /x\              4*sin(2*x)    \     -9 + x /             2*x*cos(2*x)
- 8*asin|-|*cos(2*x) - ------------- - ----------------------- + -------------
        \3/                 ________                   3/2                 3/2
                           /      2            /     2\            /     2\   
                          /      x             |    x |            |    x |   
                         /   1 - --         27*|1 - --|          9*|1 - --|   
                       \/        9             \    9 /            \    9 /
2xcos⁡(2x)9(1−x29)32−8cos⁡(2x)asin⁡(x3)−4sin⁡(2x)1−x29−(3x2x2−9−1)sin⁡(2x)27(1−x29)32\frac{2 x \cos{\left(2 x \right)}}{9 \left(1 - \frac{x^{2}}{9}\right)^{\frac{3}{2}}} - 8 \cos{\left(2 x \right)} \operatorname{asin}{\left(\frac{x}{3} \right)} - \frac{4 \sin{\left(2 x \right)}}{\sqrt{1 - \frac{x^{2}}{9}}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 9} - 1\right) \sin{\left(2 x \right)}}{27 \left(1 - \frac{x^{2}}{9}\right)^{\frac{3}{2}}}
Simplify
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