 Total derivative

ID: total-derivative

 Top articles  Latest articles + New article in topic

Total derivative by

Wikipedia Bot 0  1970-01-01

 Read the full article

Total derivative by

Ciro Santilli 35  Updated 2025-04-18  +Created 1970-01-01

The total derivative of a function assigns for every point of the domain a linear map with same domain, which is the best linear approximation to the function value around this point, i.e. the tangent plane.

E.g. in 1D:

T o t a l d er i v a t i v e = D [f (x_{0})] (x) = f (x_{0}) + \frac{\partial f}{\partial x} (x_{0}) \times x

and in 2D:

D [f (x_{0}, y_{0})] (x, y) = f (x_{0}, y_{0}) + \frac{\partial f}{\partial x} (x_{0}, y_{0}) \times x + \frac{\partial f}{\partial y} (x_{0}, y_{0}) \times y

 Read the full article

 New to topics? Read the docs here!