Производная acos(sin(3*x))

Вы ввели

acos(sin(3*x))

$$\operatorname{acos}{\left(\sin{\left(3 x \right)} \right)}$$

d                 
--(acos(sin(3*x)))
dx                

$$\frac{d}{d x} \operatorname{acos}{\left(\sin{\left(3 x \right)} \right)}$$

Первая производная

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

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

Вторая производная

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

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

Третья производная

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

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

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