... they didn't teach you basic notation?
$\dfrac {d^2 x}{{dy}^2}$ means the 2nd deriviative
$\dfrac {d^3 x}{{dy}^3}$ means the 3rd derivative
$\dfrac {d^n x}{{dy}^n}$ means the nth derivative
if it's understood you are differentiating with respect to $x$ you can use shorthand notation
$y'=\dfrac {dy}{dx}$
$y''=\dfrac {d^2 y}{{dx}^2}$
etc.