Answer
$${\text{False}}$$
Work Step by Step
$$\eqalign{
& y = \frac{{{e^x}}}{{{x^2}}},{\text{ then }}y' = \frac{{{e^x}}}{{2x}} \cr
& {\text{False, to differentiate }}y = \frac{{{e^x}}}{{{x^2}}}{\text{ we need to apply the quotient }} \cr
& {\text{rule}}{\text{.}} \cr} $$