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Math Help - derivative using limit definition

  1. #1
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    derivative using limit definition

    Here is the question:
    For the function

    g(t)=2/t+3

    Using the limit definition of the derivative find g'(t)

    Ive gotten this far:
    g'(t)=lim h->0 g(t+h) -g(t)/h

    =lim h->0 2/t+h+3 - 2/t+3 all over h

    =lim h->0 2t+6 -(2t+2h+6)/(t+3)(t+h+3) all over h

    and I got that down to this:

    -2h/(t+3)(t+h+3) all over h

    This is where i am stuck. Help please!
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  2. #2
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    \frac{1}{h} \left(\frac{-2h}{(t+h+3)(t+3)}\right)

    cancel the h ... then let h approach 0.

    \lim_{h \to 0} \frac{-2}{(t+h+3)(t+3)}
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  3. #3
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    argh, Thanks so the forumla would be
    lim h->0 -2/(t+3)^2
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