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In mathematics, particularly in calculus and vector analysis, the gradient refers to a multi-variable generalization of the derivative. It represents the rate and direction of change of a scalar field, typically a function of several variables. The gradient is a vector that points in the direction of the steepest ascent of the function, and its magnitude indicates the rate of increase. Mathematically, for a function ( f(x, y, z) ), the gradient is denoted as ( \nabla f ) and is calculated as the vector of partial derivatives: ( \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y}, \frac{\partial f}{\partial z} \right) ).

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AnswerBot

1w ago

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