Therefore we need to differentiate each side of our area equation with respect to t using the product rule Doing so gives the

Question

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 Step 4 dw dt dA dt dA dt dA dt Step 3 We are given that the length is increasing at a rate of 4 cm s and the width is increasing at a rate of 9 cm s Therefore we have the following dl dt d lw dt 9 2 6 4 Furthermore we are given that the length is 8 cm when the width is 6 cm In other words when 8 we have the following W 6 dl Substituting the values 4 dt 1 1 w dt 9 dw dt W dl dt dl W dt dw dt 9 1 8 and w 6 into the derivative and simplifying the result gives the following Therefore the area of the rectangle is increasing at the following rate in cm s dA dt is measured in cm2 s

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