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Math Help - Implicit Differentiation w/ Natural Log

  1. #1
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    Implicit Differentiation w/ Natural Log

    y + lnxy = 1

    Find dy/dx

    The answer is -y/(x(y+1))

    But I do not know How to get there.

    Thanks.
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  2. #2
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    Quote Originally Posted by r2d2 View Post
    y + lnxy = 1

    Find dy/dx

    The answer is -y/(x(y+1))

    But I do not know How to get there.

    Thanks.
    y + \ln(xy) = 1

    y + \ln(x) + \ln(y) = 1

    \frac{dy}{dx} + \frac{1}{x} + \frac{1}{y} \cdot \frac{dy}{dx} = 0

    finish the algebra and solve for \frac{dy}{dx}
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