The Chain Rule & Implicit Differentiation · Medium problem

A function $f(x,y)$ with continuous second partial derivatives has, at the point $(1, 1)$: $f_x = 2$, $f_y = -1$, $f_{xx} = 1$, $f_{xy} = 3$, $f_{yy} = 0$. Let $g(t) = f(t, t^2)$. Find $g''(1)$.