2 6.667/20 points Implicit differentiation is a special case of chain rule. The equation x3 + xy - 7 = 0 implicitly defines a function y = y(x), but it is difficult to express y as an explicit function of x. However, you can still find x via implicit differentiation. dy By doing so you get dx p(x, y) -2xy X-3x^2+y^2 ,where p(x, y): (Input functions in increasing alphabetic order) dy as a function dx Similarly, for the function z = z(x, y) implicitly defined via a + y - e = 1, you can find via implicit differentiation the partial derivatives zx (x, y) and zy(x, y), without obtaining (x, y) explicitly: X -2x/e^2z x-3y^2/e^2z q zz (x, y) = where p = and zy(x, y) = where q (In the following, input one of 'increasing, decreasing, undecided' in the boxes) decreasing From the partial derivatives obtained via implicit differentiation, one can see that when a > 0, the z = z(x, y) is with respect to x, when a