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The derivative of the function/ arcsin(sin(x)^2)

Derivative of arcsin(sin(x)^2)

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

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The solution

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