Okay, here we go!
sqrt(3x) is the same as (3x)^1/2
So use the power rule as you would any parenthetical polynomial under an exponent.
Just as the derivative of (2x + 7)^3 is (3) (2x + 7)^2 (2),
the derivative of (3x)^1/2 is (1/2) (3x)^-1/2 (3).
The (1/2) is the old parenthetical exponent, the (3x)^-1/2 is acquired by doing the power rule and subtracting one from the exponent, and the (3) comes from taking the derivative of the parenthetical argument, 3x.
So we end up with (3/2) (3x)^-1/2
Or (3/2) (sqrt(3x))^-1
Which, in taking the sqrt out of the denominator for simplest radical form by multiplying the numerator and denominator by sqrt(3x), (if you prefer), is:
[(3/2)(sqrt(3x))] / 3x
As a final move, the 3/2 and 3 reduce to 1 and 2 respectively, making the final answer:
sqrt(3x) / 2x
Hope this helps!