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Problem simplifying a power function derivation

  1. Feb 26, 2012 #1
    Hello All,

    I can compute the solution, but I fail to see how it further simplifies into the final expression. The solution manual lists both the answer and its simplified formulation.

    How do I go from step three to step four?

    1. The problem statement, all variables and given/known data

    Find the derivative of: f(x) = [itex](2x)^{\sqrt{2}}[/itex]

    2. Relevant equations

    [itex]\frac{d}{dx}[/itex]x[itex]^{r}[/itex]=r[itex]^{r-1}[/itex]

    3. The attempt at a solution

    1) f(x) = [itex](2x)^{\sqrt{2}}[/itex] = ([itex]2^{\sqrt{2}}[/itex])([itex]x^{\sqrt{2}}[/itex])

    2) Application of the product rule: g'(x)f(x) + f'(x)g(x)

    3) Answer = [itex]2^{\sqrt{2}}[/itex][itex]\sqrt{2}[/itex][itex]x^{\sqrt{2}-1}[/itex]

    4) Simplification: [itex]2\sqrt{2}[/itex][itex](2x)^{\sqrt{2}-1}[/itex]

    Many Thanks!
     
  2. jcsd
  3. Feb 26, 2012 #2
    Hello if you want us to see your writing you have type[tex] then type in {/tex} but with brackets
     
  4. Feb 26, 2012 #3
    mtayab1994, I don't exactly follow. Do you not see what I've posted? What do you mean by, "your writing"?

    Thanks
     
  5. Feb 26, 2012 #4

    Mark44

    Staff: Mentor

    I don't know what mtayab1994 was going on about - what you wrote looked perfectly clear to me.
     
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