The first thing you want to do is to convert the radicals into rational exponents, which gives you d/dx (x^(1/3) + 4x^(-1/2)). Then you can use the power rule on both of the terms to get (1/3)x^(-2/3) +4(-1/2)x^(-3/2). That simplifies to be (1/3) x^(-2/3) - 2x^(-3/2).