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Math Help - Proving the quotient rule using this definition of differentiability

  1. #1
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    Proving the quotient rule using this definition of differentiability

    Hi,
    I've been working on this problem for an hour and I don't know what I'm doing wrong where I can't solve it. Help would be very much appreciated.

    First I'm using this definition of differentiability:

    f is differentiable at a if:
    f(a+h) = f(a) + f'(a)h + E(h) where E(h)/h --> 0 as h-->0

    Now, I'm trying to show:
    If g(x) = 1/f(x) and f(a)=/=0 then we have: g'(a) = -f'(a)/[f(a)^2]

    Thanks guy
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  2. #2
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    Quote Originally Posted by AKTilted View Post
    Hi,
    I've been working on this problem for an hour and I don't know what I'm doing wrong where I can't solve it. Help would be very much appreciated.

    First I'm using this definition of differentiability:

    f is differentiable at a if:
    f(a+h) = f(a) + f'(a)h + E(h) where E(h)/h --> 0 as h-->0


    What is f, anyway? And how's f'(a) defined in your book?

    Tonio



    Now, I'm trying to show:
    If g(x) = 1/f(x) and f(a)=/=0 then we have: g'(a) = -f'(a)/[f(a)^2]

    Thanks guy
    .
    Follow Math Help Forum on Facebook and Google+

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