# What does derivated mean?

Jan 17, 2017

In the context of calculus, I think it means differentiated...

#### Explanation:

Given a function $f \left(x\right)$, if it is smooth enough we can derive another function $f ' \left(x\right)$ by the process called differentiation.

$f ' \left(x\right) = {\lim}_{h \to 0} \frac{f \left(x + h\right) - f \left(x\right)}{h}$

The resulting function $f ' \left(x\right)$ is usually called the derivative of $f \left(x\right)$.

In other fields (e.g. chemistry) one product that has been derived from another may be called a derivate. By a common (American?) practice, nouns often turn into verbs, so instead of derive, you might say derivate, meaning to make something into a derivate.

If so, then derivated is the past participle of to derivate, i.e. it means derived.

So in the context of calculus derivated probably means the same as differentiated. That is: derived by a process of differentiation.

Personally I prefer differentiated, but perhaps the apparently synthetic word derivated may be helpful in order to distinguish it from other uses of differentiated or of derived.