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Math Help - differentiation from first principles

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    differentiation from first principles

    I understand the first section of this question but i can't get to the end.

    it is differentiate from from first principles x+1/1-x

    Thanks
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  2. #2
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    Quote Originally Posted by james863 View Post
    I understand the first section of this question but i can't get to the end.

    it is differentiate from from first principles x+1/1-x

    Thanks
    f(x+h) - f(x) = \frac{1+x+h}{1-x-h} - \frac{1+x}{1-x}

    \frac{1+x+h}{1-x-h} - \frac{1+x}{1-x} = \frac{(1+x+h)(1-x) - (1+x)(1-x-h)}{(1-x-h)(1-x)}

    \frac{(1+x+h)(1-x) - (1+x)(1-x-h)}{(1-x-h)(1-x)} = \frac{2h}{(1-x-h)(1-x)}

    This means,

    \lim_{h \to 0}\frac{f(x+h) - f(x)}{h} = \lim_{h \to 0}\frac{2}{(1-x-h)(1-x)} = \frac{2}{(1-x)^2}
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