Highlights of Calculus
Highlights of Calculus (Res.18-005, MIT OCW). Instructor: Professor Gilbert Strang. Highlights of Calculus is a series of short videos that introduces the basics of calculus - how it works and why it is important. The intended audience is high school students, college students, or anyone who might need help understanding the subject. The series is divided into three sections: 1) Introduction - Why Professor Gilbert Strang created these videos, 2) Highlights of Calculus - Five videos reviewing the key topics and ideas of calculus, Applications to real-life situations and problems, and 3) Derivatives - Twelve videos focused on differential calculus, More applications to real-life situations and problems. (from ocw.mit.edu)
| Lecture 11 - Derivatives of ln y and sin-1(y) |
Make a chain of a function and its inverse: f-1(f(x)) = x starts with x and ends with x. Take the slope using the Chain Rule. On the right side the slope of x is 1. Chain Rule: dx/dy dy/dx = 1. Here this says that df-1/dy times df/dx equals 1. So the derivative of f-1(y) is 1/(df/dx). BUT you have to write df/dx in terms of y. The derivative of ln y is 1/(derivative of f = ex) = 1/ex. This is 1/y, a neat slope! Changing letters is OK : The derivative of ln x is 1/x.
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