1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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


    User Avatar
    Science Advisor
    Homework Helper

    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


    User Avatar
    Staff Emeritus
    Science Advisor

    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]
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?

Similar Discussions: Derivative of e^y
  1. Derivative of y (Replies: 4)

  2. Reflect e^x at y=2 (Replies: 8)

  3. Isolate y from e (Replies: 14)