Derivative of sin(x)*atan(x)

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

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

Simplify

                                            /         2 \       
                                            |      4*x  |       
                                          2*|-1 + ------|*sin(x)
                                            |          2|       
                  3*sin(x)   6*x*cos(x)     \     1 + x /       
-atan(x)*cos(x) - -------- - ---------- + ----------------------
                        2            2                  2       
                   1 + x     /     2\           /     2\        
                             \1 + x /           \1 + x /        

$$- \frac{6 x \cos{\left(x \right)}}{\left(x^{2} + 1\right)^{2}} - \cos{\left(x \right)} \operatorname{atan}{\left(x \right)} - \frac{3 \sin{\left(x \right)}}{x^{2} + 1} + \frac{2 \left(\frac{4 x^{2}}{x^{2} + 1} - 1\right) \sin{\left(x \right)}}{\left(x^{2} + 1\right)^{2}}$$

Simplify