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Find derivative of f(a) for f(t)=(2t+1)/(t+3) using the definition of a derivative

  1. Oct 11, 2012 #1
    1. The problem statement, all variables and given/known data

    Find derivative of f(a) for f(t)=(2t+1)/(t+3) using the definition of a derivative

    2. Relevant equations

    f '(a)=lim as x goes to a of (f(x)-f(a))/(x-a)

    3. The attempt at a solution

    f '(a)=lim as x goes to a of (f(x)-f(a))/(x-a)
    f '(a)=lim as t goes to a of (((2t+1)/(t+3))-((2a+1)/(a+3)))/(t-a)
    f '(a)=lim as t goes to a of (((2t+1)(a+3))/((t+3)(a+3)))-(((2a+1)(t+3))/((a+3)(t+3)))
    simplified and got
    f '(a)=lim as t goes to a of ((-5a+5t)/((a+3)(t+3)))/(t-a)

    I don't know where to go from here.
     
    Last edited: Oct 11, 2012
  2. jcsd
  3. Oct 11, 2012 #2

    LCKurtz

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    Re: Find derivative of f(a) for f(t)=(2t+1)/(t+3) using the definition of a derivativ

    Rewriting your last equation in readable form:$$
    \frac{-5a+5t}{(a+3)(t+3)(t-a)}$$You are almost there. Factor a 5 out of the numerator, cancel like factors, and let ##t\to a## and you will have it.
     
  4. Oct 11, 2012 #3
    Re: Find derivative of f(a) for f(t)=(2t+1)/(t+3) using the definition of a derivativ

    wow i feel dumb for not realizing that.

    thanks :)
     
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