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Math Help - Quick question on an implicit differentiation problem

  1. #1
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    Quick question on an implicit differentiation problem

    Find dy/dx for x^3y^3 - y = x

    Here's what I did;

    3x^2 3y^2 y' - y' = 1
    y'(3x^2 3y^2 - 1) = 1
    y' = 1 / (3x^2 3y^2 - 1)

    Could someone point out to me where I went wrong? The given answer is 1 - 3x^2 y^3 / (3x^3 y^2 - 1)
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  2. #2
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    Quote Originally Posted by Archduke01 View Post
    Find dy/dx for x^3y^3 - y = x

    Here's what I did;

    3x^2 3y^2 y' - y' = 1
    y'(3x^2 3y^2 - 1) = 1
    y' = 1 / (3x^2 3y^2 - 1)

    Could someone point out to me where I went wrong? The given answer is 1 - 3x^2 y^3 / (3x^3 y^2 - 1)
    You have to apply the product rule to the first term.

    \frac{d}{dx}(x^3y^3)=3x^3y^2y'+3x^2y^3

    Does this make sense?
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  3. #3
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    Quote Originally Posted by adkinsjr View Post
    You have to apply the product rule to the first term.

    \frac{d}{dx}(x^3y^3)=3x^3y^2y'+3x^2y^3

    Does this make sense?
    Ah, I get it. Stupid overlook on my part. Thanks again, broseidon.
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