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Math Help - Derivative

  1. #1
    jhb
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    Derivative

    I'm sure I am making a simple mistake...

    Find the derivative of the following  \frac {-2x}{6y^2}

    (the question actually asks for the second derivative, the equation above is the first derivative... I'm just not sure how to take the 2nd derivative).

    Thank you for your time.
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  2. #2
    Master Of Puppets
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    Do you need to find the derivative implicitly? This means for either x or y. Or are you looking for parital derivatives?
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  3. #3
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by jhb View Post
    I'm sure I am making a simple mistake...

    Find the derivative of the following  \frac {-2x}{6y^2}

    (the question actually asks for the second derivative, the equation above is the first derivative... I'm just not sure how to take the 2nd derivative).

    Thank you for your time.
    Hopefully you're differentiating with respect to x.
    \frac{d^2y}{dx^2}=\frac{d}{dx}\left(\frac{-2x}{6y^2}\right)=\frac{6y^2(-2)+2x(6)\cdot2y\frac{dy}{dx}}{(6y^2)^2}

    I think that you'll see here that you can simplify matters by substitution...
    Last edited by VonNemo19; July 27th 2009 at 05:36 PM.
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  4. #4
    jhb
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    Yeah, sorry. The question states: Using implicit differentiation, find the second derivative

    Original Equation:



    For the first derivative, I got:  \frac {-2x}{6y^2}
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  5. #5
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    Quote Originally Posted by jhb View Post
    Yeah, sorry. The question states: Using implicit differentiation, find the second derivative

    Original Equation:



    For the first derivative, I got:  \frac {-2x}{6y^2}
    in future, post the entire problem to avoid confusion.


    y' = -\frac{x}{3y^2}

    y'' = -\frac{3y^2 - 6xy \cdot y'}{9y^4}

    y'' = -\frac{3y^2 - 6xy \cdot \left(-\frac{x}{3y^2}\right)}{9y^4}<br />

    clean up the algebra
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