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derivative

derivative

6 9.6
The rate a function changes at a point
  • noun
  • /dɪˈrɪvətɪv/
  • Specialized
translation icon : derivada
  • Use the product rule to find the derivative.
  • first derivative
  • second derivative
  • partial derivative

The first thing is to take the derivative of XDX.

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Examples

  • In calculus, the derivative determines how a quantity changes as its input changes.

  • So we're going to find the derivative Y prime of P.

  • But also I can take the derivative right here.

  • And now you need a time derivative of this guy.

  • It's being the derivative of the square of X.

  • So this derivative here has to be negative.

  • Who can give me the derivative of X?

  • So now let's consider the derivative with respect to P.

  • It's the derivative of the natural log function.

  • The first thing is to take the derivative of XDX.

Synonyms

differential
vsderivative
  • Specialized
7 9.3

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

is the actual rate value at a point rather than the small change
first derivative
vsderivative
  • Specialized
1 7.9

How fast one value changes compared with another at a particular point

is the rate value found at a specific point by differentiation
differential coefficient
vsderivative
  • Specialized
9.1

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

is the single-point rate value rather than the general formula result
derived function
vsderivative
  • Specialized
7.5

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

is the rate value at a single point not the whole rule

Compounds

OTC derivative
  • Specialized
1 9.9

A financial contract privately negotiated and traded between two parties, not on an exchange

first derivative
  • Specialized
1 7.9

How fast one value changes compared with another at a particular point

1 9.9

A private financial contract made between two parties, not traded on a public exchange

derivative instrument
  • Specialized
8.7

A financial product whose value comes from something like a stock or bond

partial derivative
  • Specialized
8.7

How fast a function with two or more variables changes when one variable changes and others stay the same

How Rapid

instantaneous
35 5.1
rapid change
6 3.3
derivative
  • Specialized
6 9.6
gradual
75 3.0

Surface Forms

derivative singular
derivatives plural

Morphology

derivative = derive (semi-transparent) = derive + ative

The calculus meaning is an extension of 'something obtained from' (a function), but it is technical and may not be obvious to general learners.

Etymology

Derivative in math also comes from Latin derivare ('from' + 'stream'). A math derivative is like the amount 'drawn off' from a function at one point, and that 'drawn' amount tells you how fast the function is changing.