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Derivative (calculus) (view source)
Revision as of 21:03, September 8, 2020
, 21:03, September 8, 2020rm tag
A '''derivative''', one of the fundamental concepts of [[calculus]], measures how quickly a [[function]] changes as its input value changes. Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point. For example, the derivative of <tt>y = x<sup>2</sup></tt> at the point <tt>(1,1)</tt> tells how quickly the function is increasing at that point. If a function has a derivative at some point, it is said to be '''differentiable''' there. If a function has a derivative at every point where it is defined, we say it is a '''differentiable function'''. Differentiability implies [[continuous|continuity]].
A '''derivative''', one of the fundamental concepts of [[calculus]], measures how quickly a [[function]] changes as its input value changes. Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point. For example, the derivative of <tt>y = x<sup>2</sup></tt> at the point <tt>(1,1)</tt> tells how quickly the function is increasing at that point. If a function has a derivative at some point, it is said to be '''differentiable''' there. If a function has a derivative at every point where it is defined, we say it is a '''differentiable function'''. Differentiability implies [[continuous|continuity]].