Answer
\[\frac{{dy}}{{dx}} = \frac{{5x - 6}}{{2x\sqrt x }}\]
Work Step by Step
$$\eqalign{
& y = \frac{{5x + 6}}{{\sqrt x }} \cr
& {\text{by using the quotient rule}} \cr
& \frac{{dy}}{{dx}} = \frac{{\sqrt x \frac{d}{{dx}}\left( {5x + 6} \right) - \left( {5x + 6} \right)\frac{d}{{dx}}\left( {\sqrt x } \right)}}{{{{\left( {\sqrt x } \right)}^2}}} \cr
& {\text{find derivatives}} \cr
& \frac{{dy}}{{dx}} = \frac{{\sqrt x \left( 5 \right) - \left( {5x + 6} \right)\left( {\frac{1}{{2\sqrt x }}} \right)}}{{{{\left( {\sqrt x } \right)}^2}}} \cr
& {\text{simplifying}} \cr
& \frac{{dy}}{{dx}} = \frac{{5\sqrt x - \left( {5x + 6} \right)\left( {\frac{1}{{2\sqrt x }}} \right)}}{x} \cr
& \frac{{dy}}{{dx}} = \frac{{10{{\left( {\sqrt x } \right)}^2} - \left( {5x + 6} \right)}}{{2x\sqrt x }} \cr
& \frac{{dy}}{{dx}} = \frac{{5x - 6}}{{2x\sqrt x }} \cr} $$
