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