Practical Class 8. Review for Test "Differential Calculus of Functions of Several Variables"

This practical session is a review for the first test on differential calculus of functions of several variables. It covers four key problem types: finding the domain of a function, computing partial derivatives and the total differential, differentiating composite and implicit functions, and investigating local extrema using the second derivative test. Each topic includes a concise theoretical summary, worked examples with geometric illustrations, and practice problems. The session also provides advice on how to prepare effectively, including memorizing key formulas and practicing time management.