Partial derivative
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Definition at a point
Generic definition
Suppose is a function of more than one variable, where is one of the input variables to . Fix a choice and fix the values of all the other variables. The partial derivative of with respect to , denoted , or , is defined as the derivative at of the function that sends to at for the same fixed choice of the other input variables.
For a function of two variables
Suppose is a real-valued function of two variables , i.e., the domain of is a subset of . We define the partial derivatives as follows:
- Partial derivative with respect to :
In words, it is the derivative at of the function .
This partial derivative is also denoted or .
- Partial derivative with respect to :
In words, it is the derivative at of the function .
This partial derivative is also denoted or .
For a function of multiple variables
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