Module 3

Introduction to Derivatives

This module begins the formal study of the derivative. The first section develops the notion of the derivative as the limit of the difference quotient, which gives the slope of the tangent to a curve at any point where the tangent line exists. Differentiability as a property of a function at a specific point is presented along with a mention of its relationship to continuity. The second section presents specific ways of finding the derivative f'(x) from the original function f without using limit techniques. These methods include the power rule, product rule, quotient rule, chain rule, and implicit differentiation.

Terminologies

Differentiable- A functionf is said to be differentiable at a point x = a if f'(a) exists.

Difference Quotient- The difference quotient,