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Vector Derivatives - Definition
The derivative of a vector valued function is defined in terms of its components. We shall state the definitions for three dimensions. The two-dimensional case is similar. DEFINITION Given a vector valued function F(r) = f1(t)i + f2(t)j + f3(t)k, the derivative F'(f) is defined by F'(r) = f1'(t)i + f2'(t)j + f3'(t)k F'(t) exists if and only if f1'(t), f2'(t), and f3'(t) all exist. When we use the notation X = xi + yj + zk, the derivative is written
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Last Update: 2006-11-25