Question

How do you use the limit definition of the derivative to find the derivative of `f(x)=2/x`?

Answer 1

`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)`