Concept · from MIT 18.01SC Single Variable Calculus

The Exponential Function, its Derivative, and its Inverse

4 lecture clips
1 problem-solving video
3 problem files
Solutions by MIT (3)

About these materials

MIT's own material for this topic, in MIT's order: Session 17: The Exponential Function, its Derivative, and its Inverse.

Source: MIT OpenCourseWare 18.01SC Single Variable Calculus, Fall 2010, Prof. David Jerison — original course page on ocw.mit.edu ↗. License: CC BY-NC-SA 4.0. Order: the items appear in the order MIT's own session page lists them. Taken from MIT's published course files, downloaded from ocw.mit.edu on September 22, 2026. How RedLectern is built.

MIT 18.01SC · 1. Differentiation · Part B: Implicit Differentiation and Inverse Functions · This session on MIT OpenCourseWare ↗

Lecture Video and Notes · Video Excerpts

Clip 1: Definition of exLecture clip · 12:17–20:30 · 8:13 long · transcript Watch Notes (PDF) ↗
Clip 2: Natural LogLecture clip · 20:30–27:10 · 6:40 long · transcript Watch Notes (PDF) ↗

Worked Example

MIT's problem set

Problem Set 2

MIT places Problem Set 2 at the end of Part B: Implicit Differentiation and Inverse Functions; it covers the whole part, not only this topic. Problem Set 2 on MIT OpenCourseWare ↗

DifferentiationProblemsPDF on MIT ↗ (opens MIT OpenCourseWare in a new tab)
- 1F Chain rule, implicit differentiation: exercises 3, 5, 8a, 8c
- 1G Higher derivatives: exercises 4, 5b
- 1H Exponentials and Logarithms: Algebra: exercises 1a, 1b, 2, 3a, 5b
- 1I Exponentials and Logarithms: Calculus: exercises 1c, 1d, 1e, 1f, 1m, 4a
Integration TechniquesProblemsPDF on MIT ↗ (opens MIT OpenCourseWare in a new tab)
- 5A Inverse trigonometric functions; Hyperbolic functions: exercises 1a, 1b, 1c (just sin, cos, sec), 3f, 3g, 3h
- 5A Inverse trigonometric functions; Hyperbolic functions: exercises 5a, 5b, 5c
Use Integration Techniques (PDF) to do the problems below.: Solutions to Differentiation problemsSolution by MITPDF on MIT ↗ (opens MIT OpenCourseWare in a new tab)
Use Integration Techniques (PDF) to do the problems below.: Solutions to Integration Techniques problemsSolution by MITPDF on MIT ↗ (opens MIT OpenCourseWare in a new tab)

Where this sits in MIT 18.01SC

Open this session in the full course 18.01SC Single Variable Calculus: all units →

MIT OpenCourseWare, Prof. David Jerison, 18.01SC Single Variable Calculus, Fall 2010.

License: CC BY-NC-SA 4.0 · Edition: Fall 2010 · Open the original course on OCW ↗

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The Exponential Function, its Derivative, and its Inverse

MIT's session, in MIT's order

Lecture Video and Notes · Video Excerpts

Worked Example

Lecture Video and Notes · Video Excerpts

Recitation Video

Lecture Video and Notes · Video Excerpts

MIT's problem set

Problem Set 2

Where this sits in MIT 18.01SC

Clip 1: Definition of ex

Clip 2: Natural Log

Clip 1: Derivative of ax

Log and Exponent Derivatives

Clip 1: The Most Natural Logarithmic Function