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Math Help - Implicit differentiation with second derivative

  1. #1
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    Implicit differentiation with second derivative

    Hi everyone i can't solve this problem:

    Find if

    (The second derivative can't be expressed solely using .)


    I used implicit differentiation an found that DY/DX = -5x/3y
    So for i know i have to use the quotient rule but the answer will have y.


    Thank you
    Last edited by danicloud; November 6th 2011 at 07:00 AM.
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  2. #2
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    Re: Implicit differentiation with second derivative

    I think the point of the exercise is that it's OK to have the second derivative in terms of x and y. Note. When you have y' in your answer use the first part to eliminate it.
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    Re: Implicit differentiation with second derivative

    Thank you... yes i subsituted the first derivative but this is what i got:

    (-15y-25/y)/(3y)**2

    i don't know how to continue. Did i do something wrong??
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    Re: Implicit differentiation with second derivative

    This is what I got

    y' = -\frac{5x}{3y}
    so

    y'' = -\frac{5}{3} \frac{y - x y'}{y^2}
    Now bring in your first derivative

    y '' = - \frac{5}{3} \dfrac{ y - x \left(- \frac{5x}{3y}\right)}{y^2}

    Now simplify

    y'' = \frac{5}{9} \frac{3y^2+5x^2}{y^3}

    (Notice that you can bring in the original ellipse to simplify a little more!)
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    Re: Implicit differentiation with second derivative

    thank you but i still don't understand.

    I brought down the first derivative and i got:

    (-5/3)*[y-x*(-5/3)(x/y)]/(y^2)

    But now i don't know how to continue and simplify this. If you could explain it to me

    Thanks
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  6. #6
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    Re: Implicit differentiation with second derivative

    clear the complex fraction by multipying by \frac{3y}{3y} ...

    -\frac{5}{3} \cdot \frac{y + \frac{5x^2}{3y}}{y^2} \cdot \frac{3y}{3y}
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