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Derivative by limts

  1. Sep 21, 2008 #1
    1. The problem statement, all variables and given/known data

    lim {f(x+h)-f(x)}/h
    f(x)=4/x







    So far, i have plugged in the function, and got
    {4/(x+h)-(4/x)}/h

    I have a Ti-89, my brother no longer needed for college, and when i factored this, it gave me -4/x^2. This is also the answer supplied in the back of the book. With that being said, i have the answer for this worksheet, but i really want to know HOW to factor this. I know it is going to be showing up a whole heck of alot, with this being the definition of a derivative using limits, so i want to know how this factors. I have tried a few times, but due to the difficulty of writing math by typing, i will just say that all attempts ended in indeterminant answers, so obviously, something hasn't worked.
     
  2. jcsd
  3. Sep 21, 2008 #2

    Defennder

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    Homework Helper

    What have you done so far? You plugged in the function correctly. Now just combine everything into 1 common fraction and simplify it. Then note that (x+h) approaches x when h approaches 0.
     
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