C^r for functions of several variables indicates that all partial derivatives, both mixed and non-mixed, of order r are continuous. This definition extends the concept of C^r from single-variable functions to multivariable functions, clarifying that continuity of derivatives is essential for classification. The discussion confirms that the interpretation of C^r remains consistent across different dimensions, emphasizing the importance of continuity in multivariable calculus.
PREREQUISITESMathematicians, students of calculus, and anyone studying advanced functions in multivariable analysis will benefit from this discussion.