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How do you use the limit definition of the derivative to find the derivative of $f (x) = \frac{2}{x}$ $f(x)=2/x$ ?

1 Answer

Jul 30, 2016

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

Explanation:

$f'(x) = lim_(hrarr0) (f(x+h) - f(x))/h$

$=lim_(hrarr0) (2/(x+h) - 2/x)/h = lim_(hrarr0) ((2x - 2(x+h))/(x(x+h)))/h$

$=lim_(hrarr0)1/h (-2h)/(x(x+h)) = lim_(hrarr0) (-2)/(x(x+h)) = -(2)/(x^2)$

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