... 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.