Rewrite roots and reciprocals before using the power rule

For this expression the real domain is $x>0$: the square root requires $x\ge0$, and the reciprocal excludes 0. Write $x^{-3}-x^5+x^{3/2}$. The source root is a square root over $x^3$, not a cube root.

Apply the power and sum rules: $-3x^{-4}-5x^4+\frac32x^{1/2}$, valid for $x>0$. This is the printed answer.