What is the derivative of -3x((x+1)^1/2)

recall that to get the derivative of 2 functions of x which are multiplied, we do this:

d/dx f(x)g(x) = f'(x)g(x) + f(x)g'(x)
therefore,
d/dx 3x((x+1)^1/2) = 3(x+1)^(1/2) + (3x)*(1/2)*(x+1)^(-1/2)

hope this helps~ :)