After episode 3 of Lanterns, I’m seeing a lot of people question how Guy was eligible to receive a Green Lantern ring. This scene from Superman shows exactly why. He was ready to fight the world’s strongest meta-human. He might be a jerk, but he’s a fearless jerk and a good person at heart.
This man teaches at a community college in California.
His salary: around $800,000 a year.
The engineers who passed calculus because of him: $1,800,000 to start.
He has more calculus students than Harvard, MIT, and Stanford combined.
This is Professor Leonard's Calculus 2, Lecture 6.2. Free on YouTube.
Professor Leonard has taught calculus on YouTube for over a decade. His channel has millions of subscribers across 150 countries. Every major university has students who watch him the night before their exam.
Then the concept.
An inverse function is a machine that undoes another machine. If a function takes 2 and gives you 8, the inverse takes 8 and gives you back 2. Finding an inverse means switching every x and y in the equation and solving for y again. The graph flips across the line y = x like a mirror.
Then the problem.
Sometimes it is easy to find the inverse. Sometimes it is impossible to write it explicitly. A function like 3π sin x + sin x cannot be solved for x with algebra. You have to think. What angle makes the whole thing equal to 1? You work backwards through the unit circle until the answer appears.
Then the shortcut.
If you want the derivative of an inverse at a point, you do not need the inverse itself. You only need the derivative of the original function. The formula: the derivative of the inverse at a point equals 1 divided by the derivative of the original function evaluated at the switched point. The inverse flips the coordinates, so you flip where you plug in.
Watch the moment he shows why G prime of 8 equals 1/12 without ever writing the inverse function.
Every engineering student memorizes the derivative rules. Professor Leonard's lecture is the one that shows why the inverse derivative formula is just those same rules run backwards.
A software engineer at a semiconductor company in Austin said Professor Leonard's channel is the reason she passed Calculus 2 on her second attempt. She graduated, joined the company, and now makes $165,000 a year.
Bookmark this and watch later - after this lecture every inverse problem on your exam will feel like a question you already answered.
This 50-minute lecture by Jeff Bezos will teach you more about business than a 2-year MBA program.
Bookmark it and give it 50 minutes today, no matter what.