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Math Help - Implicit differentiation

  1. #1
    Junior Member
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    Sep 2009
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    Implicit differentiation

    Hi, I am stuck on this question.

    A ladder 8 meters long rests against a wall with its base x metres from the wall and its top y metres high. Explain why x^2+y^2=64 and differentiate the equation implicitly with respect to time. Find with three significant figures:

    a) the rate at which the top is sliding down when the base is alipping out at a constant rate of 2cm/s and is 2 meters from the wall

    b) the rate at which the base is slipping out when the top is slipping down at a constant rate of 2mm/s and is 7 meters high.

    One part i really dont get is how to differentiate with respect to time.

    Thanks
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  2. #2
    Senior Member
    Joined
    Jan 2010
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    Starting with x^2+y^2=64

    Take the derivative with respect to t:

    \implies~ \frac{d}{dt} (x^2) + \frac{d}{dt}(y^2) = \frac{d}{dt} (64)

    Can you calculate each of these terms?
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