The Chain Rule & Implicit Differentiation · Medium problem

Let $z = f(x,y)$ have continuous second partial derivatives, with $f_{xx} = 1$, $f_{xy} = 2$ and $f_{yy} = -1$ everywhere. Along the line $x = 2t$, $y = 3t$, find $\dfrac{d^2 z}{dt^2}$.