Partial derivative
From Calculus
Contents
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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