see if you can answer this one
Let f = f(u,v) and u = x + y, v = x - y
i) assume f to be twice differentiable and compute f_{xx} and f_{yy} in terms of f_{u}, f_{v}, f_{uu}, f_{uv} and f_{vv}.
ii)express the wave equation:
((∂²f)/(∂x²))-((∂²f)/(∂y²))=0
in terms of partial derivatives of f with respect to u and v.