A **covariant derivative** of a vector field in the direction of the vector denoted is defined by the following properties for any vector **v**, vector fields **u, w** and scalar functions *f* and *g*:

- is algebraically linear in so
- is additive in so
- obeys the product rule, i.e. where is defined above.

Note that at point *p* depends on the value of **v** at *p* and on values of **u** in a neighbourhood of *p* because of the last property, the product rule.

Read more about Covariant Derivative: Coordinate Description, Examples, Notation, Derivative Along Curve, Relation To Lie Derivative

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