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Mathematics vocabulary · Calculus

Derivative

Meaning in mathematics, with examples

/dɪˈrɪvətɪv/nounCore term

In mathematics, derivative means: A function that gives the rate of change of another function at each point, which is the slope of its graph there; the derivative of x² is 2x.

In Turkish: türev

How it is used

You find, take or calculate the derivative and use it to find tangents, maximum and minimum points or velocity. It is written f′(x), read 'f prime of x', or dy/dx, read 'dee y by dee x' (UK) or 'dee y dee x' (US).

Example sentences

  1. Find the derivative of f(x) = 3x² + 2x and evaluate it at x = 1.

  2. Set the derivative equal to zero to find the maximum and minimum points.

Common collocations

  • take the derivative
  • first derivative
  • second derivative
  • partial derivative
  • derivative with respect to x
  • differentiateTo find the derivative of a function, that is, a formula for its rate of change; if you differentiate x³, you get 3x².
  • slopeA number that measures how steep a line is: the change in y divided by the change in x between any two points on the line.
  • limitThe value that a function or sequence gets closer and closer to as the input approaches a certain number or grows without bound.
  • chain ruleThe rule for differentiating a function that is inside another function: the derivative of f(g(x)) is f′(g(x)) × g′(x).
  • integralThe result of integration: either a family of functions whose derivative is the given function, or a number giving the area under a curve between two limits.

This word in other fields

The same English word can have a different meaning in another field:

More terms: Calculus

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