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2.3 Vector Function of a Single Variable

Limits and derivatives and continuity of vectors can be defined exactly as for numerical functions of one variable, component by component:

second derivative

In computing such derivatives, dot products, cross products and products of numbers times vectors all obey the product rule, as in single variable calculus:

In two dimensions vectors can also be expressed in polar coordinates; in three dimensions in cylindric or spherical coordinates (and still others as well).