(calculus) fraction where the root is taken from top and bottom can i just square it to eliminate the root?

diff(sqrt(sin(1+3*x^3))/sqrt(1+x^3), x) = (9/2)*cos(1 + 3*x^3)*x^2/(sqrt(sin(1 + 3*x^3))*sqrt(1 + x^3)) - (3/2)*sqrt(sin(1 + 3*x^3))*x^2/(1 + x^3)^(3/2)