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Math Help - implicit differentiation

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    implicit differentiation

    Suppose that y is a function of x determined by e^xy = y. Find y(0) and y'(0).
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    Quote Originally Posted by myoplex11 View Post
    Suppose that y is a function of x determined by e^xy = y. Find y(0) and y'(0).
    I'm assuming this is e^{xy} = y and not e^xy = y (which would be kind of silly, I guess)?

    y(0):

    e^{0 \cdot y} = y

    y = 1

    So y(0) = 1.

    y'(0):
    e^{xy} = y

    (y + xy')e^{xy} = y'

    So at x = 0 this becomes:
    (y(0) + 0 \cdot y')e^{0 \cdot y} = y'(0)

    y(0) \cdot 1 = y'(0)

    Since y(0) = 1, thus y'(0) = 1 also.

    -Dan
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