Suppose that is a continuously differentiable function such that at every point of the plane at least one of the partial derivatives is zero.

Prove that depends on just one variable (either or ). In other words, either or .

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# Tag: product space

## Rigidity of functions

Suppose that is a continuously differentiable function such that at every point of the plane at least one of the partial derivatives is zero.

Prove that depends on just one variable (either or ). In other words, either or .