Question

How to find the derivative function of `g(x) = 3/(x-2)`? f(x)= f(x+h)-f(x) / h

Answer 1

I guess you want the derivative of `g(x)` using your definition of derivative (for `f(x)` in your question).
The complete definition is:
`lim_(h->0)(f(x+h)-f(x))/h=f'(x)`
and so:

hope it helps