Производная atan(sin(3*x))

Вы ввели

atan(sin(3*x))

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

Первая производная

  3*cos(3*x) 
-------------
       2     
1 + sin (3*x)

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

Вторая производная

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

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

Третья производная

   /           2               2              2         2     \         
   |      2*cos (3*x)     6*sin (3*x)    8*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)                              

$$\frac{27 \cos{\left (3 x \right )}}{\sin^{2}{\left (3 x \right )} + 1} \left(-1 + \frac{6 \sin^{2}{\left (3 x \right )}}{\sin^{2}{\left (3 x \right )} + 1} - \frac{2 \cos^{2}{\left (3 x \right )}}{\sin^{2}{\left (3 x \right )} + 1} + \frac{8 \sin^{2}{\left (3 x \right )} \cos^{2}{\left (3 x \right )}}{\left(\sin^{2}{\left (3 x \right )} + 1\right)^{2}}\right)$$

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