Partial Derivative

Just like the Derivative is used to analyze the behavior and properties of functions of single variable, it can also be applied to Multivariate Function to achieve the same purpose.

Definition

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Let be an Open Set and a subset of and a multivariate function . Then the partial derivative of at the point with respect to the -th variable is defined as

when the limit exists. Where is the unit vector of -th variable .

Notation

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Partital derivative with respect to can be denoted as or or or .