defining differentiability

I have this question on a mock exam paper for my university course; does anyone have any ideas of what to do?

The definition of differentiability is as follows. A function f:R --> R that is continuous in some interval around a point x=a is differentiable at x=a and has derivative f'(a) if the following limit exists,

f'(a)=lim((f(x)-f(a))/(x-a))

use this definition to prove that if two functions g:R-->R and h:R-->R are differentiable at the point x=a so is the function Ag+Bh where A and B are constants