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The Partial Jacobian Matrix and the Chain Rule for Functions on Products of Real n -Spaces
Department of Mathematics, Florida State University, Tallahassee, FL, USA
- 1 Department of Mathematics, Florida State University, Tallahassee, FL, USA
Applied Mathematics·Volume 16 (2025)·Pages 420–427·Published 11 April 2025·DOI10.4236/am.2025.164022
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Abstract
The usual chain rule is for compositions of functions from R n to R m , for some m and n . We consider functions whose domains and codomains are products of various R n ’s, and introduce the notion of a partial Jacobian matrix, using which we formulate a chain rule in this setting that should be useful for calculations as well as for some theoretical purposes.
KeywordsChain RulePartial DerivativeJacobian MatrixPartial Jacobian MatrixNormed Vector SpacesManifolds
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