For the given Partial Differential Equation, show that the function u is a solution by plugging it into the Partial Differential Equation.

$\displaystyle PDE \Rightarrow C^2u_{xx} = C^2u_{tt}$

$\displaystyle u(x, t) = A\sin{\frac{n\Pi}{Lx}} + B\sin{\frac{n\Pi}{Lx}}e^{\frac{-c^2n^}{L^2t}}$

I think i need to find the derivative of u, however, I am unsure how to find a derivative with both du/dx and du/dt in the solution.