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:ID: 3993a45d-699b-4512-93f9-ba61f498f77f
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#+title: partial derivative
#+author: Preston Pan
#+description: Let's take a slice of a larger pie.
#+options: broken-links:t
* Definition
The operator \(\frac{\partial}{\partial x_{n}}\) takes the [[id:31d3944a-cddc-496c-89a3-67a56e821de3][derivative]] of a function \(f(\vec{x})\) with respect to \(x_{n}\) in
the direction of the \(x_{n}\) axis. In other words, we take the derivative \(f(\vec{x})\) as if all variables
except \(x_{n}\) is constant; this is useful in cases where you only care about one variable.
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