Final answer:
The second mixed partial derivatives of a continuously differentiable function are equal, resulting in the expression &partial;²f/&partial;x&partial;y - &partial;²f/&partial;y&partial;x being zero.
Step-by-step explanation:
The student's question involves calculating the second mixed partial derivatives of a function f(x, y) with continuous first partials. According to Claireaux's theorem, if the second partial derivatives cross derivatives exist and are continuous, then they are equal, which means &partial;²f/&partial;x&partial;y is the same as &partial;²f/&partial;y&partial;x.
Therefore, the expression &partial;²f/&partial;x&partial;y - &partial;²f/&partial;y&partial;x equals zero, provided the second partial derivatives are continuous at the point in question. The continuous nature of the first partial derivatives in this problem suggests that the second partial derivatives are likely continuous as well, leading to the result of zero. However, it is important to check the continuity of the second partials for the specific function in question.