Verified answer

Re-write as (3x + 1)^(1/2)

d/dx[(3x + 1)^(1/2)] = 3/2*(3x + 1)^(-1/2)

The square root is just an exponent of (1/2) that is all.

Now you will have to use chain rule on this problem. The outer function is u^(1/2) and the inner function is 3x + 2. So the answer is (1/2)(3x+2)^(-1/2)(3)

So you get (3/2)(3x+2)^(-1/2)

Write

y = sqrt(3*x + 2) = (3*x + 2)^1/2

d/dx((3*x + 2)^1/2) = (1/2)*(3*x + 2)^(1/2 - 1)*3 = (3/2)*((3*x + 2)^(-1/2)) = (3/2)*1/sqrt(3*x + 2)