Can anyone see where I'm going wrong here...

So differentiate from 1st principles.

f(x) = sqrt(x)+1

f'(x) = (sqrt(x+h)+1)-(sqrt(x)+1) / h

f'(x) = x+h+1-x-1 / h(sqrt(x+h)+1)+(sqrt(x)+1)

So cancelling terms i get,

f'(x) = 1 / (sqrt(x+h)+1)+(sqrt(x)+1)

f'(x) = 1 / 2sqrt(x) + 2

This is where I'm confused, shouldn't it be

f'(x) = 1 / 2sqrt(x)