1. Limited time only! Sign up for a free 30min personal 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!

General Power Rule

  1. Jul 3, 2013 #1
    Hi all, regarding the proof of the general power rule,

    If we let [itex]y = x^r[/itex], then [itex]\ln y = r\ln x[/itex], and then by implicit differentiation
    [itex]\frac{y'}{y} = \frac{r}{x},[/itex]
    and thus it follows that
    [itex]y' = \frac{ry}{x} = \frac{rx^r}{r} = rx^{r-1}.[/itex]

    But the statement [itex]\ln y = r\ln x[/itex] also requires [itex]x>0[/itex], so does the General Power Rule only applies to positive real values of x?

    Thanks.
     
  2. jcsd
  3. Jul 3, 2013 #2

    mfb

    User Avatar
    2016 Award

    Staff: Mentor

    For negative real values of x, xr is well-defined for integer r only.
    In those cases, you can modify the proof a bit to work with negative values, too.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: General Power Rule
  1. Power rule (Replies: 9)

  2. Power rule (Replies: 10)

  3. General rule (Replies: 1)

  4. General Rule? (Replies: 2)

Loading...