Answer
$F’(x) = 2x-5-\frac{3}{2}x^{-\frac{5}{2}}$
Work Step by Step
$ F(x) = \frac{x^{4}-5x^{3}+x^{\frac{1}{2}}}{x^{2}}$
$Quotient Rule: $
$F’(x) = \frac{x^{2}(4x^{3}-15x^{2}+\frac{x^{-\frac{1}{2}}}{2})-(x^{4}-5x^{3}+x^{\frac{1}{2}})(2x)}{x^{4}} $
$ Expand: $
$ F’(x) = \frac{(2x^{5}-5x^{4}-\frac{3x^{\frac{3}{2}}}{2})}{x^{4}} $
$ Simplify: $
$ F’(x) = 2x-5-\frac{3}{2}x^{-\frac{5}{2}} $
