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Mathematics vocabulary · Calculus

Differentiate

Meaning in mathematics, with examples

/ˌdɪfəˈrenʃieɪt/verbCore term

In mathematics, differentiate means: To find the derivative of a function, that is, a formula for its rate of change; if you differentiate x³, you get 3x².

In Turkish: türev almak, türevini almak

How it is used

You differentiate a function 'with respect to' a variable: 'differentiate y with respect to x'. The process is called 'differentiation', and its main rules are the power rule, the product rule, the quotient rule and the chain rule.

Example sentences

  1. Differentiate f(x) = 5x⁴ − 2x with respect to x.

  2. If you differentiate position with respect to time, you get velocity.

Common collocations

  • differentiate with respect to x
  • differentiate twice
  • implicit differentiation
  • differentiate a function
  • 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.
  • chain ruleThe rule for differentiating a function that is inside another function: the derivative of f(g(x)) is f′(g(x)) × g′(x).
  • integrateTo find the integral of a function: either a function whose derivative is the given one, or the area under its graph between two limits.
  • limitThe value that a function or sequence gets closer and closer to as the input approaches a certain number or grows without bound.

More terms: Calculus

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