Question: Let . Let be a differentiable function . Let . Express in terms of partial derivatives of .

My Solution: Let be defined as . Then . Note that is differentiable and so is , because its component functions are differentiable. Thus their composition, is differentiable. Note that . Observe that .

We also know that and .

Thus

Thus .

Is this correct? Also, is there a faster way to do this? Also, one last question...are the partial derivatives of f taken with respect to x and y or with respect to t_1 and t_2 ? Or are they just dummy variables that I can interchange?