Introduction
Given a value – the price of gas, the pressure in a tank, or your distance from Boston – how can we describe changes in that value? Differentiation is a valuable technique for answering questions like this.
Part A: Definition and Basic Rules
- Session 1: Introduction to Derivatives
- Session 2: Examples of Derivatives
- Session 3: Derivative as Rate of Change
- Session 4: Limits and Continuity
- Session 5: Discontinuity
- Session 6: Calculating Derivatives
- Session 7: Derivatives of Sine and Cosine
- Session 8: Limits of Sine and Cosine
- Session 9: Product Rule
- Session 10: Quotient Rule
- Session 11: Chain Rule
- Session 12: Higher Derivatives
- Problem Set 1
Part B: Implicit Differentiation and Inverse Functions
- Session 13: Implicit Differentiation
- Session 14: Examples of Implicit Differentiation
- Session 15: Implicit Differentiation and Inverse Functions
- Session 16: The Derivative of ax
- Session 17: The Exponential Function, its Derivative, and its Inverse
- Session 18: Derivatives of other Exponential Functions
- Session 19: An Interesting Limit Involving e
- Session 20: Hyperbolic Trig Functions
- Problem Set 2
- Session 21: Review for Exam 1 - Computing Derivatives Using Differentiation Rules
- Session 22: Materials for Exam 1