The Chain Rule

In this video we discuss the Chain Rule and its formulation and relationship to the Jacobian matrix. We start by introducing the concept of composite functions and examine how they can be used to calculate the derivative of a simple scalar function. We then extend this idea to vector valued functions and demonstrate how the Chain Rule is related to the gradient/Jacobian of a function

Topics and timestamps:
0:00 – Introduction
4:06 – Single input single output function
16:26 – Multiple input single output function
19:52 – Formulation as a composite function
36:25 – Relationship to Jacobian matrix
40:05 – Multiple input multiple output function

#Calculus

[dsizov]

The Jacobian part is absolutely brilliant! Thanks Chris

[ebrewste]

I’ve never seen the decomposition approach. It makes deeper sense than memorizing the chain rule!

[SomeTechGuy]

The Julia language is excellent at doing work like this. You should incorporate it into your teachings.

[FatherGapon-gwyo]

I am a simple cat-I see Lum and I click play.

[dsizov]

But why should we multiply the two rates, and not, say, add them together? IMO this part is the hardest to explain

[rfo]

Thank you for your many helpful videos. Just one minor point. In the first portion, shouldn't the cubic function f be negative for negative x instead of positive as drawn in the rough graph. I only point it out because it may confuse and distract some. Thanks.

[Mandollr]

Can you make a lesson about Kalman Filter ?

[rfo]

Perhaps you meant to indicate a graph of h(u) instead of the label f(x).