Difference between revisions of "Implicit and explicit equations"
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| − | In mathematics, an implicit equation is a relation of the form {{math|1=''R''(''x''<sub>1</sub>, …, ''x<sub>n</sub>'') = 0}}, where {{mvar|R}} is a function of several variables. For example, the implicit equation of the unit circle is {{math|1=''x''<sup>2</sup> + ''y''<sup>2</sup> − 1 = 0}}. An explicit equation, on the other hand, expresses one variable in terms of one or more others. For example, {{math|''y'' = ''x''<sup>2</sup> + ''x'' − 1}} is a function that expresses the variable y in terms of x. | + | In mathematics, an implicit equation is a relation of the form {{math|1=''R''(''x''<sub>1</sub>, …, ''x<sub>n</sub>'') = 0}}, where {{mvar|R}} is a function of several variables. For example, the implicit equation of the unit circle is {{math|1=''x''<sup>2</sup> + ''y''<sup>2</sup> − 1 = 0}}. An explicit equation, on the other hand, expresses one variable in terms of one or more others. For example, {{math|1=''y'' = ''x''<sup>2</sup> + ''x'' − 1}} is a function that expresses the variable y in terms of x. |
==Resources== | ==Resources== | ||
* [http://www.mathsmutt.co.uk/files/impex.htm Differentiating Implicit and Explicit Functions], Math Mutts | * [http://www.mathsmutt.co.uk/files/impex.htm Differentiating Implicit and Explicit Functions], Math Mutts | ||
* [https://openstax.org/books/calculus-volume-1/pages/3-8-implicit-differentiation Implicit Differentiation], Openstax | * [https://openstax.org/books/calculus-volume-1/pages/3-8-implicit-differentiation Implicit Differentiation], Openstax | ||
Revision as of 16:07, 17 September 2021
In mathematics, an implicit equation is a relation of the form R(x1, …, xn) = 0, where R is a function of several variables. For example, the implicit equation of the unit circle is x2 + y2 − 1 = 0. An explicit equation, on the other hand, expresses one variable in terms of one or more others. For example, y = x2 + x − 1 is a function that expresses the variable y in terms of x.
Resources
- Differentiating Implicit and Explicit Functions, Math Mutts
- Implicit Differentiation, Openstax
