The Chain Rule
Today, we will be talking about the chain rule.
How to explain the chain rule:
The chain rule is one formula that can be used to find the derivative of two functions. It can be used to find the derivative of more than two functions, but for the purpose of this lesson, we will only focus on two.
The chain rule states the following:
In this situation, A and B are functions.
(A(B))' = (A(B)) * B'
Recall Leibniz Notation:
In Leibniz notation, this rule would be expressed as dz/dx = (dz/dy)(dy/dx)
Walking through an example:
Now that the chain rule has been explained, let's do an example!
First, note that the derivative of these two functions is d'(x)
Let's make f(x) = 4x + 3 and b(x) = 2x + 4
First, we have to solve each one separately. So:
f'(x) = 4
and
b'(x) = 2
If we are using the chain rule, then d'(x) = f'(b(x)) * b'(x)
So
d'(x) = f' (2x+ 4) (2)
And then we simplify even more to
(4)(2) = 8
Now, let's try two examples on your own
1) f(x) = 5x + 1 and g(x) = -3x + 4
2) f(x) = 7x + 8 and g(x) = 6x + 5
Answers:
1) d'(x) = -15
2) d'(x) = 42
Caitlyn, Nice job of including an example to help walk through the process of the chain rule!
ReplyDeleteI agree with Christine, you used good examples to explain the chain rule, its not an easy thing to explain but you did a good job.
ReplyDeleteYou did a really good job at explaining the chain rule. The examples were very helpful a.nd made for a better understanding of the topic
ReplyDeletehey, caitlyn,
ReplyDeletenice explanation of the chain rule. your steps are clear and the example is straightforward. there was a tiny error in the introduction of the post, though. i believe (A(B))' = (A(B)) * B' should be (A(B))' = (A'(B)) * B'. other than that, nice job!
professor little