How would you fine the relative extrema of

f(x)=x+8^-x ?

I know the first step is to find the derivative, which when I did I got
f'(x)=1+[(-1)(ln(8))(8^-x)]

Did I find the derivative correctly? And if I did, how do I find the zeroes of that??

Would I end up having to take the log of both sides, and end up with zeroes at x=.35207?