Step 2 We need to determine how fast the area of the rectangle is increasing In other words we are looking for a rate of change of the area In this problem the volume the length and the width are all functions of the time t where t is measured in seconds The rate of increase of the area with respect to time is the derivative dA The rate of increase of the length and width with respect to time are the derivatives dl dt dt respectively Therefore we need to differentiate each side of our area equation with respect to t using the product rule Doing so gives the following result where dA d lw dt dt dA dt dw dt C dl dt dA dt dw and 1 dt is measured in cm s