Practical class 2. Differentiation of Functions of Several Variables

This practical class develops skills in differentiating functions of several variables. Students learn to compute first-order partial derivatives by treating all variables except one as constants. The session covers finding the total differential, which combines partial derivatives into a linear approximation of the function's change. This tool is applied to approximate calculations near known points using small increments. A key theoretical point: while differentiability guarantees both continuity and the existence of partial derivatives, the converse is not true—a function can have partial derivatives at a point yet fail to be differentiable there. The class also includes finding equations of tangent planes and concludes with homework problems, solution tips, and review questions.