Derivative calculus question

Can someone show me calculus/algebra to prove that the derivative of f(x) =1/2 is f ' (x) =1/2 ?
I know that is the answer but if I can I would like to be able to better explain why.

The derivative of f(x) is zero if it's just 1/2, as it's a constant. If you meant x/2, just prove it using the definition of a derivative:

lim h-->0 [f(x + h) - f(x)]/h
lim h-->0 [(x + h)/2 - x/2]/h
lim h-->0 (x/2 - x/2 + h/2)/h
lim h-->0 (h/2)/2
lim h-->0 = 1/2
=1/2 (throughout the entire function)