Question

How do you use the definition of a derivative to find the derivative of `1/x`?

Answer 1

`-1/x^2`

Explanation:

using definition of a derivative:

`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)) /(x(x + h )))/h`

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

`rArr f'(x) = -1/x^2`