'Round d' Notation

Another convenient notation for the partial derivatives uses the Cyrillic lower case D, ∂, called a "round d". If z = f(x, y), we use:

Partial derivatives, like ordinary derivatives, may be represented as quotients of infinitesimals.

In ∂z/∂x, ∂x means Δx and ∂z means f_x(x, y) Δx. In ∂z/∂y, ∂y means Δy and ∂z means f_y(x, y) Δy.

Notice that ∂z has a different meaning in ∂z/∂x than it has in ∂z/∂y. For this reason we shall avoid using the symbol ∂z alone.

Partial derivatives are easily computed using the ordinary rules of differentiation with all but one variable treated as a constant.

Example 1

Example 2