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Mathematics vocabulary · Calculus

Chain rule

Meaning in mathematics, with examples

nounCommon term

In mathematics, chain rule means: The rule for differentiating a function that is inside another function: the derivative of f(g(x)) is f′(g(x)) × g′(x).

In Turkish: zincir kuralı

How it is used

Used for composite functions such as (3x + 1)⁵ or sin(x²). Teachers put it as 'differentiate the outside, keep the inside, then multiply by the derivative of the inside'. In Leibniz notation it is dy/dx = dy/du × du/dx.

Example sentences

  1. Use the chain rule to differentiate (3x + 1)⁵; the answer is 15(3x + 1)⁴.

  2. You forgot the chain rule: the derivative of sin(2x) is 2cos(2x), not cos(2x).

Common collocations

  • apply the chain rule
  • use the chain rule
  • by the chain rule
  • chain rule and product rule
  • derivativeA 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.
  • differentiateTo find the derivative of a function, that is, a formula for its rate of change; if you differentiate x³, you get 3x².
  • functionA rule that takes each input from a set and gives exactly one output, for example f(x) = 2x + 1, which doubles a number and adds one.
  • f of xThe usual spoken form of f(x), the output of a function f when the input is x; for example, if f(x) = x + 5, then 'f of 2' is 7.

More terms: Calculus

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