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

Using the quotient rule we get

$f ' \left(x\right) = \frac{{e}^{x} \cdot \left(x - 2\right)}{x} ^ 2$

Using the quotient rule again for the above we get

$f ' ' \left(x\right) = \frac{{e}^{x} \cdot \left({x}^{2} - 4 x + 6\right)}{x} ^ 4$

Footnote

The quotient rule for a function such as $f \left(x\right) = \frac{p \left(x\right)}{q \left(x\right)}$ is

$f ' \left(x\right) = \frac{p ' \left(x\right) \cdot q \left(x\right) - p \left(x\right) \cdot q ' \left(x\right)}{q \left(x\right)} ^ 2$

where $f ' \left(x\right) = \mathrm{df} \frac{x}{\mathrm{dx}}$