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How do you find the derivative of $f (x) = \frac{1}{x}$ $f(x)=1/x$ using the limit definition?

1 Answer

Jul 9, 2016

$f'(x) = -(1)/x^2$

Explanation:

$f'(x) = lim_(h->0) (f(x+h) - f(x))/h$

$= lim_(h->0) (1/(x+h) - 1/x)/h$

Resolve the numerator into one fraction:

$=lim_(h->0) ((x)/(x(x+h)) - (x+h)/(x(x+h)))/h = ((-h)/(x(x+h)))/h$

$=lim_(h->0) (-1)/(x(x+h)) = -(1)/x^2$

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