Derivative.. HELP?

Question

u = WV(1 + c) + v(cW - w)/ W + w 

Find du/dW and simplify where possible

Update : where the parameter c, called the coefficient of restitution, represents the “bounciness” of the ball in the collision.

Answer 1

u = WV(1 + c) + v(cW - w)/ W + w 

Where c is coefficient of restitution which constant value between 0 to 1 .

Consider V,v,w as costants .

u = WV(1 + c) + v(cW - w)/ W + w 

Differentiate the u with respect to W .

du/dW = V(1 + c) (1) + [(W + w)[v(c - 0)] - v(cW - w)(1) ] / (W + w)²  

                               [ derivative of  u/v = (vu' - uv') / v² ]        

du/dW = V(1 + c) + [(W + w)vc - vcW - vw ] / (W + w)²

du/dW = V(1 + c) + [Wvc+ wvc - vcW - vw ] / (W + w)²

du/dW = V(1 + c) + [ wvc - vw ] / (W + w)²

du/dW = V(1 + c) + [ wv(c - 1)] / (W + w)²