Practical Class 9. Test Paper No. 1 "Differential Calculus of Functions of Several Variables"

This test paper contains 30 variants for assessing students' knowledge of differential calculus of functions of several variables. Each variant includes four standard problems: finding the domain of a function, computing partial derivatives and the total differential, differentiating composite or implicit functions, and investigating a function of two variables for local extrema using the second derivative test. The problems cover a wide range of functions: polynomial, exponential, logarithmic, trigonometric, and their combinations. Answers for all variants are provided at the end. The test is designed for a 90-minute session and helps instructors evaluate students' mastery of key concepts such as domains, partial derivatives, chain rules, and extremum analysis.