Completely lost. What is the derivative of x+sqrt(x) or x+√x?

Question

I'm normally pretty good with these, but the algebra is escaping me at the moment. any help would be appreciated. Thanks!

I'm trying to apply the formula:

f'(x)=lim as h->0 of [f(x+h)-f(x)]/h

Answer 1

yeah. you lost me too.

Answer 2

ok... check out if this helps...

if f(x)= x^n

then f'(x) = n (x^(n-1))

your f(x)= x+√x

now when you take its derivative w.r.t. x,

the f'(x)= 1 +1/2(x)^(-1/2)