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Math Help - Finding derivative by first principles?

  1. #1
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    Finding derivative by first principles?

    How do I find the derivative of: y = 2/(2-x)

    I know that I will have to take the limit of "(f(x+h) - f(x))/h" as h approaches 0, but the algebra is really confusing me. If anyone could help, that would be much appreciated. Thanks in advance!
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  2. #2
    MHF Contributor

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    Re: Finding derivative by first principles?

    You know that f(x)= \frac{2}{2- x} so it should be easy to see that f(x+h)= \frac{2}{2- (x+h)}= \frac{2}{2- x- h}.

    Now f(x+h)- f(x)= \frac{2}{2- x- h}- \frac{2}{2- x}. You need to get "common denominators" by multiplying both numerator and denominator of the first fraction by 2- x and numerator and denominator of the second fraction by 2- x- h:
    \frac{2(2- x)}{(2-x-h)(2- x)}- \frac{2(2- x- h)}{(2- x-h)(2- x)}= \frac{(4- 2x)- (4- 2x- 2h)}{(2- x- h)(2- x)}

    Can you finish that?
    Thanks from topsquark and Oldspice1212
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