C1 on product

Stream: Is there code for X?

[Patrick Massot]

@Yury G. Kudryashov @Sebastien Gouezel do we have that a function defined on a product which has continuous partial derivatives is C¹? This should be somewhere near the mean value inequality but I can't find it.

[Yury G. Kudryashov]

Probably, we don't have facts about partial derivatives.

[Patrick Massot]

Do you mean "probably no"?

[Floris van Doorn]

I'll work on this.

[Patrick Massot]

Remember this is something specific to real numbers, it relies on the mean value inequality