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Thread: Quick Question on Implicit Differentiation

  1. #1
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    Quick Question on Implicit Differentiation

    I have the equation:

    (x^2)(y^-3) + 3 = y

    How do I go about implicitly differentiating this equation?

    EDIT: Solve for dy/dx. Sorry about that.
    Last edited by Jeavus; Mar 28th 2008 at 06:15 PM.
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  2. #2
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    Hi, Jeavus. You can probably achieve what this question wants of you, by differentiating both sides of the equation by $\displaystyle x$, assuming that $\displaystyle y$ is some function of $\displaystyle x$:

    $\displaystyle x^2 y^{-3} + 3 = y$

    $\displaystyle \Rightarrow \frac{d}{dx}\left[x^2 y^{-3} + 3\right] = \frac{d}{dx}\left[y\right] = \frac{dy}{dx}$

    $\displaystyle \Rightarrow \left( 2x y^{-3} - 3 x^2 y^{-4} \frac{dy}{dx} \right) = \frac{dy}{dx}$

    To do the last step, I used the "product rule" of differentiation.

    If you rearrange this, you should be able to work out $\displaystyle \frac{dy}{dx}$ as a function of $\displaystyle x$ and $\displaystyle y$. Hope that helps!
    Last edited by Pterid; Mar 28th 2008 at 06:24 PM. Reason: Typo in maths
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