What is a gradient in maths terms?

Answer 1

In mathematical terms, a gradient refers to the rate of change of a function with respect to its variables. In the context of a function of several variables, the gradient is a vector that points in the direction of the steepest ascent and whose magnitude represents the rate of increase in that direction. For a function ( f(x, y) ), the gradient is expressed as ( \nabla f = \left( \frac{\partial f}{\partial x}, \frac{\partial f}{\partial y} \right) ). In single-variable calculus, the gradient is simply the derivative of the function.