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If z = g(s+at) + f(s-at), let u = s+at and v=s-at, where a is a constant.

z = g(u) + f(v), [itex]\frac{∂z}{∂u}[/itex] = g'(u), [itex]\frac{∂^{2}z}{∂v∂u}[/itex] = 0?

or can ∂u and ∂v not even exist because it depends on two variables (a and t), which are the same ones as the ones v depends on.

Thanks!