and intermediate variables. 1. (6 pts) Let f(t) = In(x + 2y), where x = 3t2 and y = et. Compute d f(0). 2. Let f(x, y) = 19, where p(x, y) = x + y, q(x, y) = xy2, and r(x, y) = 3x - y. a. (6 pts) Compute the gradient vector of f, given by Vf = (fp, fq, fr). Evaluate this gradient vector at x = -1, y = 2. b. (3 pts) Use your answer in (a) to compute fx(-1, 2). c. (3 pts) Use your answer in (a) to compute fy(-1, 2). 3. Let f(r, 0) = xy + x2y3, where x = r cose and y = r sin 0. a. (6 pts) Compute fre. b. (6 pts) Compute for. Confirm that you get the same answer as in (a). 4. Let f represent any smooth function of x(s, t) and y(s, t), where x = s + t and y = s - t. (The word smooth means that the derivatives of f are defined and continuous. ) a. (6 pts) Show that (85 ) (8/) = (fz)2 - (fy)2. b. (BONUS: +3 pts) Compute 92. Simplify as much as possible