Changes of coordinates in two dimensions (such as that from x, y to r, f) are much more complicated than in one dimension. In one dimension, if we have a function f1x2 and choose to regard x as a function of some other variable u, then the derivative of f with respect to u is given by the chain rule, (a) Use the relations (8.104)(Problem 8.16) to evalu- ate the four derivatives 0x>0r,0y>0r,0x>0f, and3x + y = r and hence that f = exp1r2, evaluate 0f>0r and 0f>0f directly and check that your answers in parts (b) and (c) are correct.