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Homework Help: 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


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    Homework Helper

    \cos(\sqrt{x + h}) = \cos(\sqrt{x}(1 + h/x)^{1/2})
    and keep the first two terms of the binomial expansion of [itex](1 + h/x)^{1/2}[/itex].
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