Changes

A '''derivative''' is a measure in [[calculus]] of how functions change based on how their input values change. Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point. If a function has a derivative at some point, it is said to be '''differentiable''' there, and in general we call a function differentiable whenever it has a derivative at every point at which it is defined. Differentiability implies [[continuous|continuity]]  as well as [[integral|integrability]] on bounded [[subsets]] of the [[domain]].

A '''derivative''' is a measure in [[calculus]] of how functions change based on how their input values change. Given a graph of a [[real]] curve, the derivative at a specific point will equal the [[slope]] of the line [[tangent]] to that point. If a function has a derivative at some point, it is said to be '''differentiable''' there, and in general we call a function differentiable whenever it has a derivative at every point at which it is defined. Differentiability implies [[continuous|continuity]]  as well as [[integral|integrability]] on bounded [[subset]]s of the [[domain]].

To calculate the derivative of a function, one must use techniques from the differential branch of calculus. This branch of calculus is related to the integral branch by the first [[Fundamental Theorem of Calculus]]: ''[[differentiation]]'' (the process of finding a derivative) ''is the reverse process of [[integration]]'' (the process of finding an integral).

To calculate the derivative of a function, one must use techniques from the differential branch of calculus. This branch of calculus is related to the integral branch by the first [[Fundamental Theorem of Calculus]]: ''[[differentiation]]'' (the process of finding a derivative) ''is the reverse process of [[integration]]'' (the process of finding an integral).