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Derivative help *upgraded*

  1. Mar 6, 2013 #1
    Sorry for not showing my work on my last post, I'm on my good for nothing blackberry and apparently cannot type. My question was:
    Use first principles definition to find dy/dx:
    y=(-4/3x)
    lim
    x--> 0

    ---------
    (X,-4/3x)
    (X+h, -4/3(X+h)

    =lim»0 ((-4/3(x+h))-(-4/3x))/x+h-x

    I have gotten the answer 4/3x^2 through my proof, but I knew what the answer was (I looked at the back in frustration). I'm afraid I may have broken a few rules when I found a common denominator for the numerator ( (3)(x+h)(3x)) and worked it down to

    =lim»0 -12x+12x+12h/[3x+3h](3x)

    =lim »0 4h/3x^2h+3hx

    Any help is appreciated !!!!
     
    Last edited: Mar 6, 2013
  2. jcsd
  3. Mar 6, 2013 #2

    Dick

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    Science Advisor
    Homework Helper

    That's still pretty hard to read. You are leaving out too many parentheses. If you mean y=(-4)/(3x) then if you got (4h)/(3x^2+3xh) for the numerator then it's ok. Now the denominator is h, so divide by that and let h->0. 4/(3x^2) is correct.
     
    Last edited: Mar 6, 2013
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