THIS IS THE QUESTION

.

5. Basic properties of growth rates. Use the fact that the growth rate of a variable equals the time derivative of its log to show: (a) 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(t)] + [Y(t)/Y(t)]- (b) 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 Z(t)/Z(t) = [X(t)/X(t)] - [Y(t)/Y(t)]. (c) If Z(t) = X(t)", then Z(t)/Z(t) = aX(t)/X(t)