Question

How do you find `f'(4)` if `f(x)=2sqrt(2x)`?

Answer 1

First find the derivative:
`f'(x)=2*2/(2sqrt(2x))=2/sqrt(2x)`
consider `sqrt(2x)` as `(2x)^(1/2)` and derive it as a normal power of `n` where if you have `f(x)=x^n` then `f'(x)=nx^(n-1)` and remember to derive also the argument `2x` (Chain Rule) that gives you simply `2`.
then substitute `x=4` in it:
`f'(4)=2/sqrt(8)=2/(2sqrt(2))=1/sqrt(2)`
rationalizing =`sqrt(2)/2`