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Thread: Differentiate and Solve for variable

  1. #1
    Junior Member
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    Differentiate and Solve for variable

    Question:

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

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

    What I have so far:

    a) $\displaystyle K^\frac{1}{3}\frac{2}{3}L^\frac{-1}{3}$
    b) I am unsure, but would I would divide $\displaystyle \frac{W}{P}$ 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
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    Quote Originally Posted by mvho View Post
    Question:

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

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

    What I have so far:

    a) $\displaystyle K^\frac{1}{3}\frac{2}{3}L^\frac{-1}{3}$
    b) I am unsure, but would I would divide $\displaystyle \frac{W}{P}$ 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

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

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

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

    Then cube both sides ..
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