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The derivative of the function/ 3arcsin*cosx

Derivative of 3arcsin*cosx

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

You have entered [src] 
3*asin(x)*cos(x)
cos⁡(x)3asin⁡(x)\cos{\left(x \right)} 3 \operatorname{asin}{\left(x \right)} 
(3*asin(x))*cos(x)
The graph
02468-8-6-4-2-10105-5
Plot the graph f(x)
Plot the graph f'(x)
The first derivative [src] 
                      3*cos(x) 
-3*asin(x)*sin(x) + -----------
                       ________
                      /      2 
                    \/  1 - x
−3sin⁡(x)asin⁡(x)+3cos⁡(x)1−x2- 3 \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} + \frac{3 \cos{\left(x \right)}}{\sqrt{1 - x^{2}}}
Simplify
The second derivative [src] 
  /                    2*sin(x)      x*cos(x) \
3*|-asin(x)*cos(x) - ----------- + -----------|
  |                     ________           3/2|
  |                    /      2    /     2\   |
  \                  \/  1 - x     \1 - x /   /
3(xcos⁡(x)(1−x2)32−cos⁡(x)asin⁡(x)−2sin⁡(x)1−x2)3 \left(\frac{x \cos{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} - \cos{\left(x \right)} \operatorname{asin}{\left(x \right)} - \frac{2 \sin{\left(x \right)}}{\sqrt{1 - x^{2}}}\right)
Simplify
The third derivative [src] 
  /                               /          2 \                     \
  |                               |       3*x  |                     |
  |                               |-1 + -------|*cos(x)              |
  |                               |           2|                     |
  |                   3*cos(x)    \     -1 + x /           3*x*sin(x)|
3*|asin(x)*sin(x) - ----------- - --------------------- - -----------|
  |                    ________                3/2                3/2|
  |                   /      2         /     2\           /     2\   |
  \                 \/  1 - x          \1 - x /           \1 - x /   /
3(−3xsin⁡(x)(1−x2)32+sin⁡(x)asin⁡(x)−3cos⁡(x)1−x2−(3x2x2−1−1)cos⁡(x)(1−x2)32)3 \left(- \frac{3 x \sin{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}} + \sin{\left(x \right)} \operatorname{asin}{\left(x \right)} - \frac{3 \cos{\left(x \right)}}{\sqrt{1 - x^{2}}} - \frac{\left(\frac{3 x^{2}}{x^{2} - 1} - 1\right) \cos{\left(x \right)}}{\left(1 - x^{2}\right)^{\frac{3}{2}}}\right)
Simplify
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