Read Section 4.7 (pages 82-86). In this reading, the derivatives of the exponential and logarithmic functions are computed. otice that along the way the number e is defined in terms of a particular limit.
Watch this video. In this video, Jerison makes use of implicit differentiation at times during this lecture.
Work through problems 1-15 and 20 for Exercise 4.7. When you are done, check your answers against Appendix A.