Gradient

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In mathematics, the gradient of a real-valued differentiable function $\text{[math]}$ at a point $\text{[math]}$ is a vector in $\text{[math]}$ which points in the direction in which $\text{[math]}$ increases most rapidly. The magnitude of the gradient at $\text{[math]}$ is equal to the maximum directional derivative of $\text{[math]}$ at $\text{[math]}$ .

More precisely, the gradient of $\text{[math]}$ is the vector-field:

$\text{[math]}$

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Mathematics