
Proving Solution
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.

Re: Proving Solution
You do need to take derivatives: twice w.r.t. x, and twice w.r.t t. I would rewrite your u(x,t) for clarity. It's not clear, for example, exactly what's inside the argument of the second sin function. Use parentheses!