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Thread: Second Derivative using Implicit Differentiation

  1. #1
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    Second Derivative using Implicit Differentiation

    So we are asked to find the second derivative (implicitly) of : x^2y^2-6x=7
    So far I've been able to find the first derivative no problem.
    My first derivative is: -(x*y^2 + 3) / y*x^2
    I've verified this against two different online implicit differentiation calculators so I know I'm right to this point.
    However I need to take the derivative of this first derivative to reach my goal.
    I can not figure it out. Below I'll include two answers that have so far been marked wrong by webassign.net
    a) -(y^3*x - 6y) / x(-y^2*x + 3)

    b) (x*y^2 + 6) / (x^3*y)
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  2. #2
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    Re: Second Derivative using Implicit Differentiation

    actually you have a sign error in the first derivative

    to find the 2nd derivative just differentiate your expression for $y'$ again.

    You'll need to use the quotient rule.

    When you've done all that and simplified it solve for $y''$

    I get

    $y''(x)= \dfrac{-x^2 y(x)^2 y'(x)-3 x y'(x)+x y(x)^3-6 y(x)}{x^3 y(x)^2}$
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