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Homework Help: Derivative of e^y

  1. Jan 11, 2009 #1
    1. The problem statement, all variables and given/known data

    What is the derivative of e^y? i think i am differentiating with respect to x



    2. Relevant equations

    Derivative of y^x is y^x

    3. The attempt at a solution

    I don't know if I should use the chain rule or treat it like y^x. When i used the chain rule I got ye^y-1, but then I wondered if it should be e^y.
     
    Last edited: Jan 11, 2009
  2. jcsd
  3. Jan 11, 2009 #2

    Dick

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    The derivative with respect to y? Then sure, d/dy(e^y)=e^y. You can't use the power law d/dy(y^n)=n*y^(n-1). In one the variable y is an exponent, in the other it's not. They are very different functions.
     
  4. Jan 11, 2009 #3

    HallsofIvy

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    I don't see what y^x has to do with your original equation. y^x is not anything like e^y and yes, you should use the chain rule. But the chain rule does NOT give "ye^{y-1}"!

    The chain rule says that
    [tex]\frac{d e^y}{dx}= \frac{de^y}{dy}{dy}{dx}[/tex]
    [tex]\frac{d e^y}{dy}[/tex]
    is [itex]e^y[/itex], NOT "[itex]ye^{y-1}[/itex]". That power formula only applies to the variable to a constant power, not a constant power to a variable power.

    [tex]\frac{de^y}{dx}= \frac{de^y}{dy}\frac{dy}{dx}= e^y\frac{dy}{dx}[/itex]
     
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