This resource function is obsolete. Use the function ImplicitD instead.

Function Repository Resource:

ImplicitD (3.0.0) current version: 3.0.1 »

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 and Options

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:

In[1]:=
ResourceFunction["ImplicitD"][x^2 + y^2 == 1, D[y, x]]
Out[1]=

Compute the implicit derivative at a specific point:

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

Scope (1) 

ImplicitD treats non-input variables as constants:

In[3]:=
ResourceFunction["ImplicitD"][x^c + y^3 == 1, D[y, x]]
Out[3]=
In[4]:=
ResourceFunction["ImplicitD"][x^z + y^3 == 1, D[y, z]]
Out[4]=

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:

In[5]:=
ResourceFunction["ImplicitD"][x^3 + y^3 == 1, D[y, x]]
Out[5]=
In[6]:=
ResourceFunction["ImplicitD"][x^3 + y^3 == 1, D[y, x], "EliminateDependentVariables" -> True]
Out[6]=

Possible Issues (1) 

If the derivative of a variable that does not appear in the expression is requested, ImplicitD will return unevaluated:

In[7]:=
ResourceFunction["ImplicitD"][x^2 + y^2 == 1, D[z, x]]
Out[7]=

Publisher

Wolfram|Alpha Math Team

Version History

  • 3.0.1 – 27 March 2023
  • 3.0.0 – 23 March 2023
  • 2.0.0 – 23 March 2023
  • 1.0.0 – 10 April 2020

Related Resources

License Information