Second derivative rule for parametric descriptions

Statement

Consider a parametric description of the form $x=f(t),y=g(t)$, where $f$ and $g$ are functions of one variable. The second derivative rule states that:

${\frac {d^{2}y}{dx^{2}}}={\frac {f'(t)g''(t)-g'(t)f''(t)}{(f'(t))^{3}}}$

Facts used

1. Definition of parametric derivative
2. Quotient rule for differentiation