Representation: $\vec \nabla f$ (editing)

$\vec \nabla f$

$\vec \nabla f$

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The gradient is a vector using $\vec \nabla f$

$\vec \nabla f$

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*The Magnitude of the Gradient using $\vec \nabla f$

$\vec \nabla f$

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The gradient is a function using $\vec \nabla f$

$\vec \nabla f$

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The components of the gradient are partial derivatives using $\vec \nabla f$

$\vec \nabla f$

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The direction of the gradient is the direction of greatest increase of the function

$\vec \nabla f$

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The gradient can tell you a small change in a function in any direction (differentials edition) using $\vec \nabla f$

$\vec \nabla f$

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The gradient lives in the domain and has the same number of spatial dimensions as the original function using $\vec \nabla f$

$\vec \nabla f$

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The gradient is a local quantity using $\vec \nabla f$

$\vec \nabla f$

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The negative gradient of the electric potential is the electric field using $\vec \nabla f$

$\vec \nabla f$

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Directional Derivatives

All partial derivatives can be found as a slope of a tangent plane The components of the gradient are partial derivatives

The Master Formula

The gradient is a vector *The Direction of the Gradient *The Magnitude of the Gradient

The magnitude of the gradient is proportional to the density of contour lines The direction of the gradient is perpendicular to contour lines The gradient is a local quantity The gradient lives in the domain and has the same number of spatial dimensions as the original function

Acting out the Gradient

The gradient lives in the domain and has the same number of spatial dimensions as the original function The gradient is a local quantity