Visualizing the chain rule and product rule | Chapter 4, Essence of calculus
A visual explanation of what the chain rule and product rule are, and why they are true. Check out Brilliant: https://brilliant.org/3b1b Full series: ...
==========
In the last videos I talked about the derivatives of simple functions, things like powers of x, sin(x), and exponentials, the goal being to have a clear picture or intuition to hold in your mind that explains where these formulas come from. Most functions you use to model the world involve mixing, combining and tweaking these these simple functions in some way; so our goal now is to understand how to take derivatives of more complicated combinations; where again, I want you to have a clear picture in mind for each rule. This really boils down into three basic ways to combine functions together: Adding them, multiplying them, and putting one inside the other; also known as composing them. Sure, you could say subtracting them, but that’s really just multiplying the second by -1, then adding. Li...
==========
In the last videos I talked about the derivatives of simple functions, things like powers of x, sin(x), and exponentials, the goal being to have a clear picture or intuition to hold in your mind that explains where these formulas come from. Most functions you use to model the world involve mixing, combining and tweaking these these simple functions in some way; so our goal now is to understand how to take derivatives of more complicated combinations; where again, I want you to have a clear picture in mind for each rule. This really boils down into three basic ways to combine functions together: Adding them, multiplying them, and putting one inside the other; also known as composing them. Sure, you could say subtracting them, but that’s really just multiplying the second by -1, then adding. Li...
