# Derivatives of multivariable functions

## Partial derivatives

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Partial derivatives, introductionGraphical understanding of partial derivativesFormal definition of partial derivativesSymmetry of second partial derivatives

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## Partial derivative and gradient (articles)

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Introduction to partial derivativesSecond partial derivativesThe gradientDirectional derivatives (introduction)Directional derivatives (going deeper)

## Differentiating parametric curves

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Vector-valued functions introVector-valued functions differentiationDifferential of a vector valued functionVector valued function derivative example

## Multivariable chain rule

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Multivariable chain ruleMultivariable chain rule intuitionVector form of the multivariable chain ruleMultivariable chain rule and directional derivativesMore formal treatment of multivariable chain rule

## Curvature

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Curvature intuitionCurvature formula, part 1Curvature formula, part 2Curvature formula, part 3Curvature formula, part 4Curvature formula, part 5Curvature of a helix, part 1Curvature of a helix, part 2Curvature of a cycloid

## Partial derivatives of vector-valued functions

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Computing the partial derivative of a vector-valued functionPartial derivative of a parametric surface, part 1Partial derivative of a parametric surface, part 2Partial derivatives of vector fieldsPartial derivatives of vector fields, component by component

## Differentiating vector-valued functions (articles)

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Derivatives of vector-valued functionsCurvatureMultivariable chain rule, simple versionPartial derivatives of parametric surfaces

## Divergence

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Divergence intuition, part 1Divergence intuition, part 2Divergence formula, part 1Divergence formula, part 2Divergence exampleDivergence notation

## Curl

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2d curl intuition2d curl formula2d curl example2d curl nuanceDescribing rotation in 3d with a vector3d curl intuition, part 13d curl intuition, part 23d curl formula, part 13d curl formula, part 23d curl computation example

## Divergence and curl (articles)

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DivergenceIntuition for divergence formulaCurl warmup, fluid rotation in two dimensionsCurl, fluid rotation in three dimensions

## Laplacian

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Laplacian intuitionLaplacian computation exampleExplicit Laplacian formulaHarmonic Functions

## Jacobian

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Jacobian prerequisite knowledgeLocal linearity for a multivariable functionThe Jacobian matrixComputing a Jacobian matrixThe Jacobian Determinant

## Review practice

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