Counterexample

Is this true?

Mixed partial derivatives are always equal

No — it is false.

The counterexample

The object that kills this claim comes with Trap Analysis.

86 counterexamples are free — including most of the ones Part C leans on hardest.

Keep practicing

Execution slip

The idea was right. The computation was not.

See real exam options built on this mistake Drill statements like this

Go deeper· Explained in full in Differentiability in several variables· Asked in CSIR NET June 2025· From Functions of Several Variables › Partial derivatives, differentiability, chain rule

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