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Unit: Derivatives of multivariable functions

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Partial derivatives

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Basic partial derivativesGet 3 of 4 questions to level up!
Finding partial derivativesGet 3 of 4 questions to level up!
Higher order partial derivativesGet 3 of 4 questions to level up!

Quiz 1

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Gradient and directional derivatives

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Finding gradientsGet 3 of 4 questions to level up!
Visual gradientGet 3 of 4 questions to level up!
Finding directional derivativesGet 3 of 4 questions to level up!

Partial derivative and gradient (articles)

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Quiz 2

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Differentiating parametric curves

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Vector-valued functions differentiationGet 3 of 4 questions to level up!
Parametric velocity and speedGet 3 of 4 questions to level up!

Multivariable chain rule

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Multivariable chain rule introGet 3 of 4 questions to level up!
Multivariable chain ruleGet 3 of 4 questions to level up!

Quiz 3

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Curvature

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Partial derivatives of vector-valued functions

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Visual parametric surfacesGet 3 of 4 questions to level up!
Partial derivatives of vector valued functionsGet 3 of 4 questions to level up!

Differentiating vector-valued functions (articles)

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Divergence

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Visual divergenceGet 3 of 4 questions to level up!
Finding divergenceGet 3 of 4 questions to level up!

Quiz 4

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Curl

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Visual curlGet 3 of 4 questions to level up!
Finding curl in 2DGet 3 of 4 questions to level up!
Finding curl in 3DGet 3 of 4 questions to level up!
Symbols practice: The gradientGet 3 of 4 questions to level up!

Divergence and curl (articles)

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Quiz 5

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Laplacian

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Finding the LaplacianGet 3 of 4 questions to level up!

Jacobian

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Finding the JacobianGet 3 of 4 questions to level up!
Jacobian determinantGet 3 of 4 questions to level up!

Quiz 6

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Unit test

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About this unit

What does it mean to take the derivative of a function whose input lives in multiple dimensions? What about when its output is a vector? Here we go over many different ways to extend the idea of a derivative to higher dimensions, including partial derivatives, directional derivatives, the gradient, vector derivatives, divergence, curl, and more!