# What is the derivative of f(x)=(e^(1/x))/x^2 ?

$f ' \left(x\right) = \frac{- \frac{1}{x} ^ 2 {e}^{\frac{1}{x}} \cdot {x}^{2} - {e}^{\frac{1}{x}} \cdot 2 x}{{\left({x}^{2}\right)}^{2}}$
by cancelling out ${x}^{2}$ in the numerator,
$= \frac{- {e}^{\frac{1}{x}} - 2 x {e}^{\frac{1}{x}}}{{x}^{4}}$
by factoring out $- {e}^{\frac{1}{x}}$ from the numerator,
$= - \frac{\left(1 - 2 x\right) {e}^{\frac{1}{x}}}{{x}^{4}}$