# Thread: Higher Order Mixed Partial Derivatives

1. ## Higher Order Mixed Partial Derivatives

If f∈C³(S) for open S⊆R^n and f: S -> R^m, prove that all the third order mixed partial derivatives are equal.

My textbook has the proof for the second order mixed partial derivatives, but the third order seems harder.

Or can I somehow reduce the problem to the second partial derivative problem and use the fact that all the second order mixed partial derivatives are equal to prove this?

Thank you