\partial∂, called “del”, is used to distinguish partial derivatives from ordinary single-variable derivatives.
|Symbol||Informal understanding||Formal understanding|
|A tiny nudge in the direction.||A limiting variable which goes to , and will be added to the first component of the function’s input.|
|The resulting change in the output of after the nudge.||The difference between and , taken in the same limit as .|
The gradient of a function , denoted as , is the collection of all its partial derivatives into a vector.
The most important thing to remember about the gradient:
Example differential operators