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How do you find the derivative of #f(x)=1/x# using the limit definition?

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Euan S. Share
Jul 9, 2016

Answer:

#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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