Question

How do you find f'(x) using the definition of a derivative `f(x)= 1/x`?

Answer 1

Use limit definition of derivative to find:

`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)`

`= lim_(h->0) ((x-(x+h))/(hx(x+h)))`

`= lim_(h->0) ((-h)/(hx(x+h)))`

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

`=-1/x^2`