We can view as a function of a vector variable. The key insight is to use the dot product of vectors.ĭefinition as a function Generic definition ![]() It turns out that that definition can more readily be generalized to functions of vector variables. To rectify this, we revisit what the definition of the derivative says. Unfortunately, the above notation does not make direct sense because it is not permissible to divide a scalar by a vector. Intuitively, we want to define the gradient vector analogously to the derivative of a function of one variable, i.e., as the limit of the difference quotient: Note on why the epsilon-delta definition is necessary
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