The dimensions X&Y of an object are related to its volume V by the formula V equal four X ^2 y. So the first part says what happens if X is a constant. So we're going to take the derivative in terms of time of the volume equaling 4X squared, the derivative in terms of time of the Y. So we'd get DVDT equaling four X ^2 d YDT. The next part says what if Y is the constant? So we'd have the derivative in terms of time of the volume equaling 4 Y because that's the constant times the derivative in terms of T of X ^2. So DVDT would equal 4Y2XD XDT or DVDT equals 8X YDXDT. The last part says complete the equation for when neither X nor Y is constant. So DVDT is going to have to be the product rule of both X&Y. So four times the derivative in terms of time of X ^2 times the Y + 4 X squared times the derivative in terms of T of the Y or DVDT equal 8X YDXD t + 4 X squared DYDT. What they're trying to emphasize in this problem is you could think of doing the product role as making one be a constant times the derivative of the other plus the other a constant times the derivative of the 1st.