How do you find derivative of f(x) = 1/ (x+2) using the definition of the derivative?

1 Answer
Oct 14, 2015

Have a look:

Explanation:

From the definition of derivative you have:
f'(x)=lim_(h->0)(f(x+h)-f(x))/h where h is a small increment;
and in our case:
f'(x)=lim_(h->0)(1/(x+h+2)-1/(x+2))/h=
=lim_(h->0)1/h((x+2-x-h-2)/((x+h+2)(x+2)))=
=lim_(h->0)1/cancel(h)(-cancel(h)/((x+h+2)(x+2)))=
=-1/((x+0+2)(x+2))==-1/(x+2)^2