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ZixuanZhang
ZixuanZhang
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Partial Derivative

The partial derivative of with respect to at fixed is

Definition 3.2 (Partial Derivative)

Given a function of several variables, e.g. , the partial derivative of with respect to at fixed is

Roughly speaking, this is the slope of when moving in the positive direction.

can be defined similarly.

Example

Example 3.3

Consider . Then

We can similarly calculate higher derivatives.

Also, we can do mixed derivatives.

Related

Stated in

Partial Derivative | IA Groups