Производная asin(3*cos(x))

Вы ввели

asin(3*cos(x))

$$\operatorname{asin}{\left (3 \cos{\left (x \right )} \right )}$$

Первая производная

    -3*sin(x)     
------------------
   _______________
  /          2    
\/  1 - 9*cos (x) 

$$- \frac{3 \sin{\left (x \right )}}{\sqrt{- 9 \cos^{2}{\left (x \right )} + 1}}$$

Вторая производная

  /            2     \       
  |       9*sin (x)  |       
3*|-1 + -------------|*cos(x)
  |              2   |       
  \     1 - 9*cos (x)/       
-----------------------------
         _______________     
        /          2         
      \/  1 - 9*cos (x)      

$$\frac{3 \cos{\left (x \right )}}{\sqrt{- 9 \cos^{2}{\left (x \right )} + 1}} \left(-1 + \frac{9 \sin^{2}{\left (x \right )}}{- 9 \cos^{2}{\left (x \right )} + 1}\right)$$

Третья производная

  /           2                2              2       2   \       
  |      9*sin (x)       27*cos (x)    243*cos (x)*sin (x)|       
3*|1 - ------------- + ------------- - -------------------|*sin(x)
  |             2               2                       2 |       
  |    1 - 9*cos (x)   1 - 9*cos (x)     /         2   \  |       
  \                                      \1 - 9*cos (x)/  /       
------------------------------------------------------------------
                           _______________                        
                          /          2                            
                        \/  1 - 9*cos (x)                         

$$\frac{3 \sin{\left (x \right )}}{\sqrt{- 9 \cos^{2}{\left (x \right )} + 1}} \left(1 - \frac{9 \sin^{2}{\left (x \right )}}{- 9 \cos^{2}{\left (x \right )} + 1} + \frac{27 \cos^{2}{\left (x \right )}}{- 9 \cos^{2}{\left (x \right )} + 1} - \frac{243 \sin^{2}{\left (x \right )} \cos^{2}{\left (x \right )}}{\left(- 9 \cos^{2}{\left (x \right )} + 1\right)^{2}}\right)$$

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