The Chain Rule & Implicit Differentiation · Hard problem

A differentiable function $w = f(x,y)$ satisfies $f(1,2) = 5$, $f_x(1,2) = 3$, and $f_y(1,2) = -2$. A particle's position is $x(t) = t^2$, $y(t) = t+1$, so it passes through $(1,2)$ at $t=1$. Use the chain rule and a linear approximation to estimate $w$ at $t=1.1$.