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Math Help - First and second derivative question :)

  1. #1
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    First and second derivative question :)

    Find dy/dx and d^2y/dx^2 as functions of x and y given that xy^2+y=1.

    Thank you
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  2. #2
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    did you try doing it?
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  3. #3
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    Attempt

    I did yes.. a poor attempt.
    xy^2+y=1
    d/dx[xy^2+y]
    y^2dy/dx+y
    dy/dx=-y/y^2
    dy/dx=-1/y
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  4. #4
    Forum Admin topsquark's Avatar
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    Quote Originally Posted by lyoung View Post
    I did yes.. a poor attempt.
    xy^2+y=1
    d/dx[xy^2+y]
    y^2dy/dx+y
    dy/dx=-y/y^2
    dy/dx=-1/y
    You did the derivative of the first term wrong. And you never took the derivative of the last term on the LHS.
    d/dx(xy^2 + y) = y^2 + 2xy*y' + y'

    -Dan
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  5. #5
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    Where does the +y' come from? Is it not a negative?
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  6. #6
    Senior Member bugatti79's Avatar
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    Quote Originally Posted by lyoung View Post
    Where does the +y' come from? Is it not a negative?
    If you multiply out the LHS side of Dan's line in post 4 before differentiating you get

    d/dx(xy^2) + d/dx(y).

    Now differentiate this and you will get the RHS of Dan's post 4.
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