9 Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of its log to Show: 0 The growth rate of the product of two variables equals the sum of their growth rates. That is, if Z(t) =_ X(t)Y(t), then Z(t)/Z(t) = [X(t)/X(f)] + [Y(t)/Y(t)]- 9 The growth rate of the ratio of two variables equals the difference of their growth rates. That is, if Z(t) = X(t)/Y(t), then Zia/2m = [X(r)/X(r)1 [Yin/mn- 9 If Z(t) = X(r)\