Hello everyone, first post here. 1. The problem statement, all variables and given/known data Let f(x,y)=x2y+y2x , where x=sin2t and y=cos2t. Use the chain rule to compute df/dt 2. Relevant equations f(x,y)=x2y+y2x x=sin2t y=cos2t 3. The attempt at a solution This is pretty much the exact wording of the question, it's a little vague, and I'm not sure if I'm supposed to sub in sin2t and cos2t in the f(x,y) equation I did it by calculating the partial derivatives of f with respect to x and y thus finding the gradient of f, I then found the gradient at any time t by subbing in the x/y equations above into the gradient, I then calculated dx/dt and dy/dt to give the velocity vector in the x/y plane. Finally I calculated the dot product of this velocity vector and the gradient vector and ended up with a pretty long equation as my answer: 2 sin(t)cos(t)(cos4t-sin4t). I'm pretty sure this is the correct answer assuming my method and interpretation of the question is right. However I'm wondering if I could have taken a short-cut by initaially subbing in the x/y functions into f thus making f(x,y) into f(t), differentiating it with respect to t. I did this (in Maple), and ended up with a different answer which gave a different answer when I substituted in an arbitrary value for t. I'm finding it quite hard to visualize this question and I hope someone can help shed some light on it (exam January) Thanks!