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Thread: [SOLVED] Implicit Differentiation

  1. March 9th 2009, 04:49 PM #1
    edge
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    [SOLVED] Implicit Differentiation

    x^3 * y^3 - y = x

    help please

    differentiate implicitly with respect to x...
    Last edited by Jhevon; March 9th 2009 at 06:09 PM.
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  2. March 9th 2009, 05:57 PM #2
    GaloisTheory1
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    Quote Originally Posted by edge View Post
    x^3 * y^3 - y = x

    help please
    x^3 \cdot 3y^2 \frac{dy}{dx} + y^3 \cdot 3x^2 - \frac{dy}{dx}=1

    remember to use product rule on the first.
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  3. March 9th 2009, 07:05 PM #3
    edge
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    Solve for dy/dx?

    Okay, thanks... now just to make sure I'm doing this right, how would you solve for dy/dx?
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  4. March 9th 2009, 07:08 PM #4
    GaloisTheory1
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    Quote Originally Posted by GaloisTheory1 View Post
    x^3 \cdot 3y^2 \frac{dy}{dx} + y^3 \cdot 3x^2 - \frac{dy}{dx}=1

    remember to use product rule on the first.
    x^3 \cdot 3y^2 \frac{dy}{dx} + y^3 \cdot 3x^2 - \frac{dy}{dx}=1

    so

    \frac{dy}{dx}=\frac{1-y^3 \cdot 3x^2}{x^3 \cdot 3y^2-1}
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