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Young's theorem: Corresponding cross partial derivatives are equal. (To read more about Young's theorem, see Simon & Blume, Mathematics for Economists, Mixed Partials – Young's Theorem theorem is due to W. H. Young [1], but his proof is hard to follow. Suppose the partial derivatives. Week 2 of the Course is devoted to the main concepts of differentiation, to use and apply mathematics by working with concrete examples and exercises.Under the assumption that both mixed partial derivatives of f exist and are continuous at (a,b), then we can take the limit as (h,k)>(0,0) of both sides of (3) Young's Theorem : statement: > Let f be a scalar field defined in some neighbourhood of a point (a, b) er sot. is both the partial order derivatives. In this unit you will study Euler's, Schwarz's and Young's theorems, In Unit 5 you have seen yme examples of functions whose partial derivatives fx, fy. respect to y twice, and then differentiating with respect to x, etc. In this manner we can find nth-order partial derivatives of a function. Theorem. ?2f. This is sometimes known as Schwarz's theorem, Clairaut's theorem, or Young's theorem. In the context of partial differential equations it is called the Schwarz