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Glite Dictionary
first derivative

first derivative

1 7.9
How fast one value changes compared with another at a particular point
  • noun
  • /fɜrst dɪˈrɪvətɪv/
  • Specialized
translation icon : primera derivada
  • To find the maximum point of the graph, we need to analyze the first derivative.
  • first derivative of the envelope

That is not volatile because if you take the first derivative of this, you have a flat line.

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Examples

  • We also know that the slope of the curve at any point is equal to the first derivative of the curve with respect to T.

    Blog text (29)

  • The first derivative of the envelope was computed by the difference between consecutive samples.

    Academic text (2012)

  • So it will be the first derivative of X.

  • Now we're seeing sign changes in the first derivative.

    Academic text (1994)

  • This function does not give a constant after the first derivative.

    Blog text (9)

  • Our technique uses the first derivative of the envelope as a basis.

    Academic text (2012)

  • So where the first derivative with respect to X vanishes, the result you get is this.

    Sabine Hossenfelder

  • Mathematically speaking, it's the first derivative of the options price with respect to the underlying.

  • Based on the results in Table 3, the first derivative with respect to the relative military to civilian compensation (relwagec) is 0.615.

    Academic text (1998)

  • The first derivative of a function shows how quickly its values change at any point.

Synonyms

differential
vsfirst derivative
  • Specialized
7 9.3

A very small change in a number used to show how fast it changes, like dy or dx

is the function giving rate across the variable, not just a single quantity
derivative
vsfirst derivative
  • Specialized
6 9.6

The rate a function changes at a point

is the function describing instantaneous rate across the domain, not only one point
differential coefficient
vsfirst derivative
  • Specialized
9.1

The rate at which a curve goes up or down at one point

is the function found by differentiating once over the variable
derived function
vsfirst derivative
  • Specialized
7.5

A function that shows the slope of another function at each point

is the function produced specifically by a single differentiation

Surface Forms

first derivative singular
first derivatives plural

Morphology

first + derivative

The phrase is a straightforward adjective+noun composition: 'first' indicates order and 'derivative' names the rate-of-change function, so 'first derivative' clearly means the derivative taken once. This compositional pattern is regular and cross-linguistically common (e.g., Spanish 'primera derivada'), so a learner who already knows both constituent meanings can infer the MWE.

Etymology

First derivative comes from math: first means you take one step to find change, and derivative is the result you get from that step. Imagine watching a car and asking how fast its speed is changing at one moment — the first derivative tells that 'rate of change', so it means how quickly one thing changes compared to another.