An Etymological Dictionary of Astronomy and Astrophysics
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The function F(x) is called the antiderivative of the function f(x) on the interval [a,b] if at all points of this interval F'(x) = f(x). Same as primitive.

→ anti- + → derivative.

Karyâ, → function; noxostin "primitive," → first.

1) General: Derived from another; not original or primitive.
2) Math.: For a → function  y = f(x), the → limit of the → ratio of the → increment of the function, Δy, to the increment of the → variable, Δx, as the latter tends to → zero. Derived function; result of → differentiation.
3) Chemistry: Substance derived or prepared from some other → substance.

From M.E. derivatif, from L.L. derivativus, from derivat(us), p.p. of derivare, → derive + -ivus.

Vâxané, noun from vâxan, present stem of vâxanidan, → derive.

The simplest mathematical → differentiation of one quantity relative to another; df(x)/dx. It is the same as → derivative, contrasted with the → second derivative or the nth derivative.

→ first; → derivative.

In → calculus, a method for determining whether an → inflection point is a → local minimum, → local maximum, or neither.

→ first; → derivative; → test.

For a → function with several → variables, the derivative, done only once, with respect to one of the variables. For example ∂u/∂x for u = u(x,y).

→ first; → order; → partial; → derivative.

The derivative of a function of two or more variables, e.g., z = f(x,y), with respect to one of the variables, the others being considered constants (denoted ∂z / ∂x).

→ partial; → derivative.

The rate at which the rotation period of a → pulsar changes over time. This quantity, dP/dT, can range from as small as 0.05 picoseconds per year (1.5 x 10^-21 seconds per second) to as large as about 10 milliseconds per year (4.2 x 10^-10 seconds per second). For the → Crab pulsar, the period derivative is 4.2 x 10^-13 s s^-1, implying a decrease in the star's → rotation energy of about 4.5 x 10³⁸ erg s^-1. Period derivative is a very important parameter for the determination of the pulsar age.

→ period; → derivative.

In → calculus, the → derivative of a → first derivative. It is usually written as f''(x), d²y/d²x, or y''.

→ second; → derivative.

A method, used in → calculus, for determining whether a given → stationary point of a → function is a → local minimum or → local maximum.

→ second; → derivative; → test.