Question

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

Answer 1

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`