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Math Help - Differentiate and Solve for variable

  1. #1
    Junior Member
    Joined
    May 2009
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    Differentiate and Solve for variable

    Question:

    The function Y=K^\frac{1}{3}L^\frac{2}{3} is Given.

    a) Find \frac{dY}{dL}
    b) Solve for "L" in the equation: \frac{2}{3}K^\frac{1}{3}L^\frac{-1}{3}=\frac{W}{P}

    What I have so far:

    a) K^\frac{1}{3}\frac{2}{3}L^\frac{-1}{3}
    b) I am unsure, but would I would divide \frac{W}{P} by K. Only thing is, I am sure you can't just ignore that exponent can you?

    Help! I need a refresher. That much is obvious.
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  2. #2
    MHF Contributor
    Joined
    Sep 2008
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    West Malaysia
    Posts
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    Quote Originally Posted by mvho View Post
    Question:

    The function Y=K^\frac{1}{3}L^\frac{2}{3} is Given.

    a) Find \frac{dY}{dL}
    b) Solve for "L" in the equation: \frac{2}{3}K^\frac{1}{3}L^\frac{-1}{3}=\frac{W}{P}

    What I have so far:

    a) K^\frac{1}{3}\frac{2}{3}L^\frac{-1}{3}
    b) I am unsure, but would I would divide \frac{W}{P} by K. Only thing is, I am sure you can't just ignore that exponent can you?

    Help! I need a refresher. That much is obvious.
    HI

    \frac{2k^{-\frac{1}{3}}}{3L^{-\frac{1}{3}}}=\frac{W}{P}

    3WL^{\frac{1}{3}}=2Pk^{\frac{1}{3}}

    L^{\frac{1}{3}}=\frac{2Pk^{\frac{1}{3}}}{3W}

    Then cube both sides ..
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