In the problems of rates in the application of derivates always look at the units of rates given, in this question the rates have units of distance/time.
= - 5 cm/minute, = + 4 cm/minute, (at x = 8, y = 6) = ?
There are two sides of rectangle x and y, so the area of the rectangle will be A = xy, and we have to calculate the rate of change of area with time.
A = x y
Differentiating both sides,
= 6( - 5) + 8(4) = - 30 + 32 = 2 cm2/minute.
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