Derived Function

What is Derived Function?

The function that gives the gradient of a curve at every point of its domain, written f dashed of x or dy by dx. Its value at a particular x is the gradient of the tangent to the curve at that point, and equivalently the instantaneous rate at which y is changing with respect to x there. It is obtained as the limiting value of the gradient of a chord as the horizontal separation of the chord's two endpoints shrinks towards zero. For Cambridge O Level Additional Mathematics 4037 only an informal understanding of this limiting process is required; differentiation from first principles is not examinable.

This definition is part of the Calculus chapter in Cambridge O Level Additional Mathematics.

Concepts related to Derived Function

• gradient of a tangent
• instantaneous rate of change
• limit of a chord gradient