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Implicit differentiation

  1. Jul 22, 2011 #1
    1. The problem statement, all variables and given/known data
    find the d^2y/dx^2 if y^3 + y = 2 cos x at the point (0,1)


    2. Relevant equations



    3. The attempt at a solution

    my dy/dx = (-2 sin x)/(3y^2 + 1)

    I don't know how to find d^2y/dx^2?
    And when and how will I use the oint (0,1)?
     
  2. jcsd
  3. Jul 22, 2011 #2

    ehild

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    Differentiate both sides of the equation twice with respect to x, using chain rule on the left-hand size (differentiate with respect to y first than with respect to x).

    ehild
     
  4. Jul 22, 2011 #3
    oh.. so I have..

    3y^2 * y' + y' = -2 sin x

    y'(3y^2 + 1) = -2 sin x

    y' = (-2 sin x)/(3y^2 + 1)

    Right?
     
  5. Jul 22, 2011 #4

    ehild

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    It is right. Get the second differential. But differentiate both sides of the equation y'(3y^2 + 1) = -2 sin x instead of the last one. It will be an easier process.

    ehild
     
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