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!

How to find the derivative of y= x^-1/e^-x

  1. Jan 31, 2009 #1
    1. The problem statement, all variables and given/known data
    y = ((x)^−1) (e^−x)

    3. The attempt at a solution

    Solving this out i got
    [(x^-1) - (x^-2)] e^-x

    however the book is telling me the answer is
    −(x^−1 + x^−2)e^−x

    wouldnt that give me (-x^−1 - x^−2)e^−x ??
    what did i do wrong??
  2. jcsd
  3. Jan 31, 2009 #2


    Staff: Mentor

    Re: Differentiate

    Apparently you lost a sign somewhere. I'm guessing that you forgot the factor of (-1) when you differentiated e^(-x).
    [tex]d/dx(x^{-1}e^{-x}) = x^{-1} e^{-x} (-1) - x^{-2}e^{-x}[/tex]
    [tex]= -x^{-1}e^{-x} - x^{-2} e^{-x}[/tex]
    which agrees with the book's answer.

    BTW, you're not "solving this out;" you're differentiating this function or calculating the derivative of the given function.
  4. Jan 31, 2009 #3
    Re: Differentiate

    Thanks i thought the derivative of e^-x stayed the same
  5. Jan 31, 2009 #4


    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    Re: Differentiate

    [tex]\frac{d}{dx}e^x = e^x[/tex]

    However, in general (using the chain rule)

    [tex]\frac{d}{dx} e^{f\left(x\right)} = f^\prime\left(x\right)e^{f\left(x\right)}[/tex]

    In your case

    [tex]f\left(x\right) = -x[/tex]


    [tex]\frac{d}{dx}e^{-x} = \frac{d}{dx}\left(-x\right)e^{-x} = - e^{-x}[/tex]

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

Have something to add?

Similar Discussions: How to find the derivative of y= x^-1/e^-x