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Math Help - Partial differentiation

  1. #1
    Senior Member Pinkk's Avatar
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    Partial differentiation

    Let V =\pi r^{2}h, S = 2\pi r(r+h)

    Compute the following

    \frac{\partial V}{\partial h}|_{S}, \frac{\partial V}{\partial S}|_{r}, \frac{\partial S}{\partial V}|_{r}

    That is for the first partial derivative hold S constant and so on for the other two partial derivatives.

    So for the first one, am I suppose to solve V in terms of S? I am not sure how to go about computing those partial derivatives. Thank you.
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  2. #2
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    <br />
\frac{\partial V}{\partial h}|_{S}<br />
    You must have V(S,h).
    Eliminate r from V(r,h) using S(r,h).
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  3. #3
    Senior Member Pinkk's Avatar
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    And how would I go about doing that, exactly? Since a r^{2} and a r appear in the expression of S.
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  4. #4
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    Please solve a quadratic equation or look here
    Quadratic equation - Wikipedia, the free encyclopedia
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