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!

Derivation by first principles: cos(x^0.5)

  1. Aug 28, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of the function f(x)=cos(√x) by first principles

    2. Relevant equations

    f'(x)= lim as h tends to zero of [f(x+h)-f(x)]/h

    3. The attempt at a solution

    Problems arise immediately, since I have no idea what to do with the expression cos(√(x+h)), I've tried binomial expansion, but to no avail. Any help would be greatly appreciated
     
  2. jcsd
  3. Aug 28, 2013 #2

    pasmith

    User Avatar
    Homework Helper

    [tex]
    \cos(\sqrt{x + h}) = \cos(\sqrt{x}(1 + h/x)^{1/2})
    [/tex]
    and keep the first two terms of the binomial expansion of [itex](1 + h/x)^{1/2}[/itex].
     
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: Derivation by first principles: cos(x^0.5)
  1. Deriving cos(x)^ln(x)? (Replies: 7)

Loading...