An Etymological Dictionary of Astronomy and Astrophysics
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فرهنگ ریشه شناختی اخترشناسی-اخترفیزیک

M. Heydari-Malayeri    -    Paris Observatory

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Number of Results: 9 Search : derivative
antiderivative
  کریای ِ نخستین   
karyâ-ye noxostin

Fr.: primitive   

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.

derivative
  واخنه   
vâxané

Fr.: 1) dérivé; 2; 3) dérivée   

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.

first derivative
  واخنه‌ی ِ نخست   
vâxane-ye naxost

Fr.: dérivée première   

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.

first derivative test
  آزمون ِ واخنه‌ی ِ نخست   
âzmun-e vâxane-ye naxost

Fr.: teste de la dérivée première   

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

first; → derivative; → test.

first-order partial derivative
  واخنه‌ی ِ پاری ِ رایه‌ی ِ نخست   
vâxane-ye pâri-ye râye-ye naxost

Fr.: dérivée partielle du premier degré   

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.

partial derivative
  واخنه‌ی ِ پاری   
vâxane-ye pâri

Fr.: dérivée partielle   

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.

period derivative
  واخنه‌ی ِ دوره   
vâxane-ye dowré

Fr.: dérivée de la période   

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.

second derivative
  واخنه‌ی ِ دوم   
vâxane-ye dovom

Fr.: dérivée seconde   

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

second; → derivative.

second derivative test
  آزمون ِ واخنه‌ی ِ دوم   
âzmun-e vâxane-ye dovom

Fr.: test de la dérivée seconde   

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.