The Chain Rule & Implicit Differentiation · Challenge problem

At the point $(1, 1)$ a smooth function $f(x,y)$ has $f_x = 2$, $f_y = 3$, $f_{xx} = 4$, $f_{xy} = -1$, $f_{yy} = 5$. Let $u(r,\theta) = f(r\cos\theta, r\sin\theta)$. Find $u_{\theta\theta}$ at $r = \sqrt2$, $\theta = \dfrac{\pi}{4}$.