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Math Help - Comparison of Two Derivatives

  1. #1
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    Comparison of Two Derivatives

    There's this equation that I have stumbled whilst working on several exercise questions.



    I'm sorry that I post this in image, I've tried to write it down using Latex but it shows Error in preview mode.

    The instruction is compare the derivative of P in respect to t with the derivative of P in respect to D. I have tried to solve it but my end calculation shows 9/DT instead of what it is supposed to be in the answer key, which is -D/T. I'm a bit confused here, what I'm doing wrong?

    Thank You
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  2. #2
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    I'm going call the stuff within the parentheses for A since it does not depend on t or D.

    Then we have \frac{dP}{dt}=\frac{3At^2}{D^3} and \frac{dP}{dD}=\frac{-3At^3}{D^4}

    Comparing the two we see that \frac{-D}{t}\cdot \frac{dP}{dD}=\frac{3At^2}{D^3}=\frac{dP}{dt}
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  3. #3
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    Quote Originally Posted by Mondreus View Post
    I'm going call the stuff within the parentheses for A since it does not depend on t or D.

    Then we have \frac{dP}{dt}=\frac{3At^2}{D^3} and \frac{dP}{dD}=\frac{-3At^3}{D^4}

    Comparing the two we see that \frac{-D}{t}\cdot \frac{dP}{dD}=\frac{3At^2}{D^3}=\frac{dP}{dt}
    Ah ok thanks, I forgot to add the minus in differentiating the D^3.
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