Derivation is the process of deriving a sentence from the start symbol S according to a grammar.

Relationship to Parse Tree

Notations for a Derivation

Symbol => is used to denote a derivation step.
=>* is used to denote derivation in zero or more steps.
=>+ is used to denote derivation in one or more steps.

Definition of a language in Terms of Derivations

Leftmost derivation : the leftmost nonterminal is replaced in each step. If S=>*(lm) a then a is called a left-sentential form of the grammar G. A leftmost derivation is traced by a predictive, top-down parser.
Rightmost derivation canonical derivation : the right most nonterminal is replaced in each step. A shift-reduce parser traces a rightmost derivation “backwards"

Citation:

• Aho, Lam, Sethi, & Ullman, Compilers: Principles, Techniques, and Tools
• UT Austin CS375: Compilers by G.Novak.