Scribe! The Chain Rule, and song

Hi this is Van, and doing the weekly scribe. So, let's get this started. Yay!, no pictures to put in or make!, I love my job, anyways onto the scribe.



So, we started the class off with our 4 question, multiple choice quiz. 8 minutes long. Then we did practice questions. Which were:

a f(x) = 4x³- 1x²+5x - 7

b g(x) = (2x² - 1) ( x³ - 4x + 3)

c h(x) = 2x - 3
x² - 4

This is our first class after spring break, so I completely forgot about the Product rule and Quotient rule. So Mr. K teaches us a song that helps us remember them both. Here it goes.

The quotient rule you wish to know is lowdy high minus highdy low.
Put a line and down below
Denominator squared will go
The product rule you have in rhyme
Is one prime two plus one two prime

You sing it in a way, that makes it sound like twinkle twinkle little star.

So after the questions we are given a question that looks like this

x²-3x

We've never dealt with a problem like this before. So, we apply Function DeComposition and it looks like this.

f(x) = x
g(x) = x²-3x

We are then given a rule. For situations like this. It's called the Chain Rule. And the chain rule says this:

F(x) = f(g(x))
F'(x) = f'(g(x)) - g'(x)

So we implement this new found rule onto our question.

F(x) = x² - 3x
= (x²-3x)^½

f(x) = x^½
g(x) = x² - 3x
f'(x) = ½ x^½
g'(x) = 2x - 3

F'(x) = ½(x² - 3x)^-½ ٠ 2x - 3


So, after we went through our first example, we did another one

h(x) = (x³ - 3x)²
h(x) = f(g(x))
h'(x) = 2(x³ - 3x)(3x²-3)
= 2[3x^5 - 12x³ + 9x
= 6x^5 - 24x³ + 18x

That was using our chain rule. Here's if we do it manually without the chain rule.

h(x) = (x³ - 3x)(x³ - 3x)
= x^6 - 6x^4 + 9x²
h'(x) = 6x^5 - 24x³ + 18x

It may look easier, but Mr. K says, use the chain rule. It will be much more efficient when you advance further into Calculus.

Homework in the white and orange book is... all questions up to and including Page 77 and in the blue book is page 20.

Thank you, and next scribe can only be one other person... Temesgen. (2 person class, wee)

once again, I don't know how to place square roots over things. Annoying