Math 2.0

Real functions Functions of several real variables Concept

Gradient

Builds on Partial derivativeDifferentiable function of several variables

Summary

Let ff be a differentiable real-valued function on an open subset of ℝn\mathbb{R}^n. Its gradient at a point aa is the vector ∇f(a)\nabla f(a) of its partial derivatives at aa. It points in the direction in which ff increases fastest, and its length is that fastest rate of increase. The derivative of ff at aa is the dot product with the gradient: Df(a)(v)=∇f(a)⋅vDf(a)(v) = \nabla f(a) \cdot v.

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Euclidean space, object, no evidence levelEuclidean spaceobjectFunction, concept, no evidence levelFunctionconceptTotal derivative, concept, no evidence levelTotal derivativeconceptFunction of several variables, concept, no evidence levelFunction of several v…conceptDifferentiable function of several variables, concept, no evidence levelDifferentiable functi…conceptPartial derivative, concept, no evidence levelPartial derivativeconceptGradient, concept, no evidence levelGradientconcept
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  1. Euclidean space object
  2. Function concept
  3. Total derivative concept
  4. Function of several variables concept
  5. Differentiable function of several variables concept
  6. Partial derivative concept
  7. Gradient concept

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191 pages build on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Gradient, lead section
About this page
Tag0ABK9V9Y64
URIm2://0ABK9V9Y64
Aliasesgradient-vector, grad
Kindconcept
WritingW1 stated
MSC26B12
UsesPartial derivative, Differentiable function of several variables
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