Product rule for differentiation of dot product

From Calculus
Jump to: navigation, search

Statement

Statement for vector-valued functions of a single variable

Version type Statement
Specific point, named functions Suppose f and g are n-dimensional. vector-valued functions of a single variable and x_0 is a point in the domain such that \! f'(x_0) and \! g'(x_0) both exist (again, as n-dimensional vectors). Then (f \cdot g)'(x_0) = f'(x_0) \cdot g(x_0) + f(x_0) \cdot g'(x_0) where \cdot denotes the dot product.