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Math Help - rate of change

  1. #1
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    rate of change

    Find the rate of change of change of x with respect to p:

    p=\sqrt \frac {500-x}{2x} , 0<x<500

    If you could guide me through this problem that would be great.
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by hemi View Post
    Find the rate of change of change of x with respect to p:

    p=\sqrt \frac {500-x}{2x} , 0<x<500

    If you could guide me through this problem that would be great.

    rate of change can be viewed as slope geometrically. now certainly you want the instantaneous rate of change of x with respect to p.

    ie \frac{dx}{dp} known as the derivative of x with respect to p.

    so let's find the slope. remember that the p is shown respect here so it is our variable.

    im not sure how far into calc you are but i'll do it the long way

    p^2=\frac{500-x}{2x}

    2p^2x+x=500

    x(2p^2+1)=500

    x=\frac{500}{2p^2+1}

    now we take the derivative

    inst. rate of change =x'=\frac{dx}{dp}=\frac{d}{dp}\left[\frac{500}{2p^2+1}\right]=\frac{(2p^2+1)0-500(4p)}{(2p^2+1)^2}
    Last edited by mr fantastic; June 12th 2009 at 05:07 AM. Reason: Made the square brackets bigger
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