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Need Help With Derivative Function

  1. Feb 12, 2008 #1
    1. The problem statement, all variables and given/known data
    Find the Derivative Function of (4x - x[tex]^{2}[/tex])


    3. The attempt at a solution

    using formula:

    [tex]
    \frac{dy}{dx} = \frac{f(x + \Delta x) - f(x)}{\Delta x}
    [/tex]



    [tex]
    \frac{4(x + \Delta x) - (-x^{2})}{\Delta x}
    [/tex]

    [tex]
    \frac{4x + 4(\Delta x) + x^{2}}{\Delta x}
    [/tex]

    Not sure where to go from here..
     
    Last edited: Feb 12, 2008
  2. jcsd
  3. Feb 12, 2008 #2

    EnumaElish

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    Let d = [itex]\Delta[/itex]x.

    f(x+d) - f(x) = 4(x+d)-(x+d)^2 - 4x + x^2

    which simplifies to (4 - d - 2x)d (you should derive this). The rest should be easy.
     
  4. Feb 12, 2008 #3

    CompuChip

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    First of all, you mean
    [tex]
    \frac{dy}{dx} = \lim_{\Delta x \to 0} \frac{f(x + \Delta x) - f(x)}{\Delta x}
    [/tex]
    as what you gave is just the difference quotient
    [tex]
    \frac{\Delta y}{\Delta x} = \frac{f(x + \Delta x) - f(x)}{\Delta x}
    [/tex]

    Not sure how you got there in the first place. If I plug [itex]f(x) = 4x - x^2[/itex] into the formula you gave, I get
    [tex] \frac{ [ 4(x + \Delta x) - (x + \Delta x)^2 ] - [4 x - x^2 ] }{ \Delta x }
    = \frac{ 4 x + 4 \Delta x - x^2 - 2 x \Delta x - (\Delta x)^2 - 4 x + x^2 }{ \Delta x}
    [/tex]
    which has some terms you don't have. Now try again.
     
  5. Feb 12, 2008 #4

    HallsofIvy

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    That's because you haven't finished the algebra! You have 4x and -4x in the numerator! You have -x2 and x2 in the numerator!
     
  6. Feb 12, 2008 #5

    CompuChip

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    Exactly, and the -4x and -x2 just happen to be some of the terms kwikness is missing :smile:
    But I'm leaving him some work.
     
  7. Feb 12, 2008 #6
    Thanks, when I wrote it down I was missing a part of the equation. Gahhh! I always make stupid mistakes like that.
     
  8. Feb 12, 2008 #7
    You could just have used the Power Rule, but I guess you haven't learned it yet.
     
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