Answer
$y'=\dfrac{3}{2}x^{1/2}+2x^{-1/2}-\dfrac{3}{2}x^{-3/2}$
Work Step by Step
Reduce the expression
$y=\dfrac{x^2+4x+3}{\sqrt{x}}=\dfrac{x^2+4x+3}{x^{1/2}}$
$y=\dfrac{x^2}{x^{1/2}}+\dfrac{4x}{x^{1/2}}+\dfrac{3}{x^{1/2}}$
$y=x^{3/2}+4x^{1/2}+3x^{-1/2}$
Then apply power rule to derivate
$y'=(\dfrac{3}{2})x^{3/2-1}+4(\dfrac{1}{2})x^{1/2-1}-3(\dfrac{1}{2})x^{-1/2-1}$
$y'=\dfrac{3}{2}x^{1/2}+2x^{-1/2}-\dfrac{3}{2}x^{-3/2}$
