Problem 1.45. As an illustration of why it matters which variables you hold fixed when taking partial derivatives, consider the following mathematical example. Let " = ry and a = yz. (a) Write w purely in terms of r and s, and then purely in terms of y and z. (b) Compute the partial derivatives and and show that they are not equal. (Hint: To compute (Ow/Or) , use a formula for w in terms of a and y, not z. Similarly, compute (Ow/82) ; from a formula for w in terms of only r and z.) (c) Compute the other four partial derivatives of w (two each with respect to y and z), and show that it matters which variable is held fixed