The Chain Rule & Implicit Differentiation · Medium problem

Two waves traveling in opposite directions along a string combine to give $w(x,t) = \sin(x-2t) + \cos(x+2t)$. The wave equation requires $w_{tt}=c^2w_{xx}$ for a constant $c^2$ (the squared wave speed). Using the chain rule to compute $w_{tt}$ and $w_{xx}$ at $(x,t) = \left(\pi, \dfrac{\pi}{4}\right)$, find $c^2 = w_{tt}/w_{xx}$ at that point.