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Homework Help: Derivatives, chain rule

  1. Nov 9, 2013 #1
    1. Find the derivative of y=e[itex]\sqrt{x}[/itex]

    2. Relevant equations

    Chain rule

    3. The attempt at a solution

    y=eu

    [itex]\frac{dy}{du}[/itex]
    = ueu-1


    u=[itex]\sqrt{x}[/itex]

    [itex]\frac{du}{dx}[/itex]= [itex]\frac{1}{2}[/itex]x-1/2

    [itex]\frac{dy}{dx}[/itex]= [itex]\sqrt{x}[/itex]e[itex]\sqrt{x}[/itex]-1 × [itex]\frac{1}{2}[/itex]x-1/2

    = [itex]\sqrt{x}[/itex] [itex]\frac{e^\sqrt{x}}{e}[/itex] × [itex]\frac{1}{2\sqrt{x}}[/itex]

    = [itex]\frac{e^\sqrt{x}}{2e}[/itex]

    The answer to this question is [itex]\frac{e^\sqrt{x}}{2\sqrt{x}}[/itex]. What did I do wrong?

    Any help is much appreciated.
     
    Last edited: Nov 9, 2013
  2. jcsd
  3. Nov 9, 2013 #2
    Nevermind, I got it.

    The derivative of e^x is still e^x.
     
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