When did the word "derivative" come into use in calculus, and why?
As in Can the word "derive" be used to mean "take the derivative of"? the word "derivative" in normal English means "stemming from". But $\int f$ "derives" from $f$ just as much as does $f'$, and $f'$ "integrates" information from $f$ just as much as does $f'$. So who decided that a ratio of fluxions should be called the derivative, and why?
The word originates from the French noun "Dérivée" (a feminine noun) introduced by Lagrange in the 18th century. One sometimes speaks of "deriving" a function but more commonly of "differentiating" it, because the term "derive" is commonly used in the logical sense of "obtaining as a consequence". To answer your question specifically, it seems to have been Joseph-Louis Lagrange who "decided" this.