I am working with the chain rule in multivariable calculus and I am having some difficulty with the question:
Let $f,g : \Bbb R \longrightarrow \Bbb R$ where $f$ and $g$ are twice differentiable. Show that $u(x,t)=f(x-at)+g(x+at)$ is a solution to the wave equation $u_{tt} = a^2 u_{xx}$.
Any help would be greatly appreciated! Thanks!