1) First question

Use the Chain Rule to find Oz/as and Oz/at. z = e cos(0), r = st, 0 = 58 + +8 = Oz = atThe temperature ata point (X, y) is T(X, y), measured in degrees Celsius. A bug crawls so that its position after t seconds is given by X : \\f 7 + t, y : 1 + %E, where X and y are measured in centimeters. The temperature function satisfies Tx(3, 2) : 2 and Ty(3, 2) : 1. How fast is the temperature rising on the bug's path after 2 seconds? (Round your answer to two decimal places.) :lw Assume that all the given functions have continuous second-order partial derivatives. If z = f(x, y), where x = 2r cos(0) and y = 2r sin(0), find the following. oz (a) ar az Oz az + ar ax az (b ) ae az az Oz + ae ax ay (c) azz ar de az + az + + azz ay2 2x2 ay ox = ax ar de ay