Производная asin(cos(2*x))

Вы ввели

asin(cos(2*x))

$$\operatorname{asin}{\left(\cos{\left(2 x \right)} \right)}$$

d                 
--(asin(cos(2*x)))
dx                

$$\frac{d}{d x} \operatorname{asin}{\left(\cos{\left(2 x \right)} \right)}$$

Первая производная

   -2*sin(2*x)    
------------------
   _______________
  /        2      
\/  1 - cos (2*x) 

$$- \frac{2 \sin{\left(2 x \right)}}{\sqrt{1 - \cos^{2}{\left(2 x \right)}}}$$

Вторая производная

  /          2       \         
  |       sin (2*x)  |         
4*|-1 + -------------|*cos(2*x)
  |            2     |         
  \     1 - cos (2*x)/         
-------------------------------
          _______________      
         /        2            
       \/  1 - cos (2*x)       

$$\frac{4 \left(-1 + \frac{\sin^{2}{\left(2 x \right)}}{1 - \cos^{2}{\left(2 x \right)}}\right) \cos{\left(2 x \right)}}{\sqrt{1 - \cos^{2}{\left(2 x \right)}}}$$

Третья производная

  /         2                2              2         2     \         
  |      sin (2*x)      3*cos (2*x)    3*cos (2*x)*sin (2*x)|         
8*|1 - ------------- + ------------- - ---------------------|*sin(2*x)
  |           2               2                          2  |         
  |    1 - cos (2*x)   1 - cos (2*x)      /       2     \   |         
  \                                       \1 - cos (2*x)/   /         
----------------------------------------------------------------------
                             _______________                          
                            /        2                                
                          \/  1 - cos (2*x)                           

$$\frac{8 \cdot \left(1 - \frac{\sin^{2}{\left(2 x \right)}}{1 - \cos^{2}{\left(2 x \right)}} + \frac{3 \cos^{2}{\left(2 x \right)}}{1 - \cos^{2}{\left(2 x \right)}} - \frac{3 \sin^{2}{\left(2 x \right)} \cos^{2}{\left(2 x \right)}}{\left(1 - \cos^{2}{\left(2 x \right)}\right)^{2}}\right) \sin{\left(2 x \right)}}{\sqrt{1 - \cos^{2}{\left(2 x \right)}}}$$

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