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Derivative question

  1. Feb 5, 2009 #1
    Our teacher wants us to find derivatives the long way

    f(x+h) - (fx) / h

    So anyways, on one of my questions 3 / x + 2 , x=8

    I know how to find the derivative of 3 / x+2 , but why was their an x=8 next to it? Am I supposed to plug this in after finding the derivative?
     
  2. jcsd
  3. Feb 5, 2009 #2
    yes, you need to plug it in for x after you find the derivative.
     
  4. Feb 5, 2009 #3

    HallsofIvy

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    I disagree with mathstudent88. The basic definition of 'derivative' is 'derivative at a given point'. From what you say, I imagine your teacher is expecting you to put it directly into the definition of the derivative of f at x0:
    [tex]\lim_{h\rightarrow 0} \frac{f(x_0+ h)- f(x_0)}{h}[/tex]
    which, for f(x)= 3/(x+2), at x0= 8 is
    [tex]\lim_{h\rightarrow 0}\frac{3/((8+h)+2)- 3/(8+2)}{h}[/tex]
    [tex]= \lim_{h\rightarrow 0}\frac{3/(10+h)- 3/10}{h}[/tex]
     
    Last edited: Feb 5, 2009
  5. Feb 5, 2009 #4

    Office_Shredder

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    With the obvious substitution of x=8 instead of x=2
     
  6. Feb 5, 2009 #5

    HallsofIvy

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    Thanks, OfficeShredder, I've edited that mistake. (So, now I can pretend I never made it!)
     
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