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Homework Help: Help finding the derivative of (e^xy)

  1. Nov 20, 2011 #1
    1. The problem statement, all variables and given/known data

    y= e^xy
    y'= ?

    2. Relevant equations

    y' [a^x] = lna(a^x)
    y' [uv] = uv' + vu'

    3. The attempt at a solution

    y = e^xy
    lny = lne^xy
    lny = xy(lne) = xy
    (1/y)y' = (x)(y') + (y)(1)
    y' = xy(y') + y^2

    From here I don't know how to isolate the derivative. (And I feel like I shouldn't have done this implicitly...)
  2. jcsd
  3. Nov 20, 2011 #2


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    Homework Helper

    Looks like you're fine so far. Now move the xy(y') term to the left-hand side and factor out the y'. Can you go on from there?
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