Производная atan(x)*sin(x)

Вы ввели

atan(x)*sin(x)

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

Первая производная

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

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

Вторая производная

                  2*cos(x)   2*x*sin(x)
-atan(x)*sin(x) + -------- - ----------
                        2            2 
                   1 + x     /     2\  
                             \1 + x /  

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

Третья производная

                                                         2       
                  3*sin(x)    2*sin(x)   6*x*cos(x)   8*x *sin(x)
-atan(x)*cos(x) - -------- - --------- - ---------- + -----------
                        2            2           2             3 
                   1 + x     /     2\    /     2\      /     2\  
                             \1 + x /    \1 + x /      \1 + x /  

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