Answer
$$\frac{{dy}}{{dx}} = \frac{{20 - {x^2}}}{{{{\left( {{x^2} - 9x + 20} \right)}^2}}}$$
Work Step by Step
$$\eqalign{
& y = \frac{x}{{\left( {x - 5} \right)\left( {x - 4} \right)}} \cr
& {\text{Simplify the denominator}} \cr
& y = \frac{x}{{{x^2} - 9x + 20}} \cr
& {\text{Differentiate}} \cr
& \frac{{dy}}{{dx}} = \frac{d}{{dx}}\left[ {\frac{x}{{{x^2} - 9x + 20}}} \right] \cr
& {\text{By the quotient rule}} \cr
& \frac{{dy}}{{dx}} = \frac{{\left( {{x^2} - 9x + 20} \right)\left( 1 \right) - x\left( {2x - 9} \right)}}{{{{\left( {{x^2} - 9x + 20} \right)}^2}}} \cr
& {\text{Simplifying}} \cr
& \frac{{dy}}{{dx}} = \frac{{{x^2} - 9x + 20 - 2{x^2} + 9x}}{{{{\left( {{x^2} - 9x + 20} \right)}^2}}} \cr
& \frac{{dy}}{{dx}} = \frac{{20 - {x^2}}}{{{{\left( {{x^2} - 9x + 20} \right)}^2}}} \cr} $$
