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'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:

11_partial_differentiation-164.gif

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

In ∂z/∂x, ∂x means Δx and ∂z means fx(x, y) Δx. In ∂z/∂y, ∂y means Δy and ∂z means fy(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


Last Update: 2011-01-22