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 derive a number to the power x (e.g. 2^x)

  1. Oct 7, 2009 #1
    i recently started my calculus III course but i was stuck with the derivative part when i derive a real number to the power x ( like 2^x) and also when deriving x^x. does anybody have an idea or a link in which these kinds of derivatives can be solved. thanks for ur help
  2. jcsd
  3. Oct 7, 2009 #2


    User Avatar
    Science Advisor

    Use "logarithmic differentiation". If [itex]y= x^x[/itex], then [itex]ln(y)= ln(x^x)= xln(x)[/itex]. Use the chain rule to differentiate ln(y) with respect to x (y'/y) and use the product rule on the right. Then solve for y'.
  4. Oct 7, 2009 #3


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    2x = ex ln(2)
  5. Oct 13, 2009 #4
    thx a lot guys that was so helpful
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook