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Math Help - rate of change of an area

  1. #1
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    rate of change of an area

    I am asked to find the rate of change of the area of a rectangle, given it's length is 15 ft, and increasing at 3 ft/sec, and it's width is 6 ft, increasing at 2 ft/sec.

    Rate of change of the area (dA) should just be the product of the other two rates (dx*dy) right? or am I missing something? Please help.
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  2. #2
    Eater of Worlds
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    The area is given by A=LW

    Therefore, by the product rule: \frac{dA}{dt}=L\frac{dW}{dt}+W\frac{dL}{dt}

    \frac{dA}{dt}=15(2)+6(3)=48
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  3. #3
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    hmmm... I am unfamiliar with this rule. Or at least, I may need a refresher to remember it.
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