ImplicitD

Source Notebook

Compute the derivative y' as a function of x from an implicit equation in those variables

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["ImplicitD"][eqn,D[y,x]]

returns the implicit derivative ∂y/∂x as determined from equation eqn.

ResourceFunction["ImplicitD"][eqn,D[y,x],pt]

returns the implicit derivative ∂y/∂x at the point pt.

Details

With "EliminateDependentVariables"→True, ResourceFunction["ImplicitD"] will attempt to eliminate the dependent variable from the output expression by substituting its original value from the input equation.

ResourceFunction["ImplicitD"] has the attribute HoldRest, so that the D[y,x] argument does not autoevaluate to 0.

Examples

Basic Examples (2)

Compute the implicit derivative ∂y/∂x on the unit circle:

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Compute the implicit derivative at a specific point:

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$ResourceFunction["ImplicitD"][x^2 + y^2 == 1, D[y, x], {0, 1}]$

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Scope (1)

ImplicitD treats non-input variables as constants:

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Options (1)

With "EliminateDependentVariables"→True, ImplicitD will attempt to eliminate the dependent variable from the output expression by substituting its original value from the input equation:

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