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Math Help - Implicit differentiation

  1. #1
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    Implicit differentiation

    Stuck on this: A curve has the equation x^2 - 4xy = y - 7x. Find the gradient at the point (2,2).
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  2. #2
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    Quote Originally Posted by Beard View Post
    Stuck on this: A curve has the equation x^2 - 4xy = y - 7x. Find the gradient at the point (2,2).
    You can differentiate both sides with respect to x remembering that y is a function of x.

    2x - 4y - 4xy' = y' - 7

    (N.B> I used the product rule on the second term (4xy)' = 4y + 4xy')

    Simplifying you get

    y' = \frac{7+2x-4y}{4x+1}

    Now just substitute x=2, y=2 and you have the value of y', which is the gradient.

    HTH
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