derivation

A map $D:C^{\infty }\to \mathbb{R}$ is a derivation at a point $x$ if it is

• linear
• follows the “Liebnitz rule” aka the product rule. For a point $x$,

$$D(fg)=D(f)g(x)+f(x)D(g)$$

If we don’t look at a single point, instead look at all points on a manifold we get that a derivation is a map

$D:C^{\infty }\to C^{\infty }$

References

@lee2013 - Chapter 3