Leibniz rule

Definition

A function $$f:A\rightarrow B$$ is said to satisfy the Leibniz rule if:

$$f(ab)=af(b)+bf(a)$$

It usually involves a lot of abuse of notation and a letter that is an operator.

Example

Take: $$D:C^\infty_p(\mathbb{R}^n)\rightarrow\mathbb{R}$$ - a Derivation if it is also $\mathbb{R}-$Linear then:

$$D(fg) = fDg + gDf$$ - which the reader should recognise as the product rule from calculus.

See also

• Derivation