Stage 36 · Limits, Derivatives & Their Applications

36.3.4 The Derivative Function: The Derivative Is a Function Too

36.3 What a Derivative Really Is: Concept and Geometry

Point 4 of 5

36.3.4 The Derivative Function: The Derivative Is a Function Too

Core idea

Every point has its own steepness, so connect them all up and you get a new function f′(x).

Module goal. Promote the derivative from "a number at one point" to "a brand-new function," and nail down its geometric meaning once and for all: the slope of the tangent.
eastmath.com · 36.3 What a Derivative Really Is: Concept and Geometry · 36.3.4 The Derivative Function: The Derivative Is a Function Too