if you are given f(x,y)=x^2+y^2 and y=cos(t) x=sin(t), then when you differentiate f with respect to t, you use the partial derivatives of f with respect to x and y in the process. When i was taught partial derivatives, i was told that we "keep all but one of the independent variables fixed.....". Now in this case, when differentiating f with respect to y, say, i dont see how this works. For, x (=cos(t) ) cannot be fixed while y (=sin(t) ) varies, can it? When we differentiate f do we 'forget' that x and y are functions of t, and treat them as independent?