Let / and w represent the length and width of the rectangle in cm, and let A represent the area of the rectangle in cm². Writing an equation for A in terms of/ and w gives the following result. A = 96cm 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 dt dA d(/w) dt dt l ur dA dt dt 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 is measured in cm²/s. dt = = dw 1) dr + ([ dt dw dt dl dt and respectively.