# arrow_back What is the Schwartz theorem?

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What is the Schwartz theorem?

Schwarz Theorem, also known as the "equality of mixed partials". It's one of the classical #calculus results, and a relief for students.

If the second derivatives of a function $\mathrm{f}: \mathbb{R}^{2} \rightarrow \mathbb{R}$ exist and
are continuous, then
$$\frac{\partial^{2} f}{\partial x \partial y}=\frac{\partial^{2} f}{\partial y \partial x}$$
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