## Tuesday, October 17, 2006

### Section 3.2: The Product and Quotient Rules

Wassup!!!

Section 3.2 is all about using 2 new rules to find derivatives more quickly. These 2 rules are known as the: 1)Product Rule 2)Quotient Rule.

1. The Product Rule: [h'(x) = [f(x) x g(x)]] = [[f(x) x g'(x)] + [g(x) x f'(x)]]

The product rule is quite simple. If one is trying to find the derivative of the product of 2 different functions, finding the product of the 1st function[f(x)] and the derivative of the 2nd function[g'(x)] plus the product of the 2nd function[g(x)] and the derivative of the 1st function[f'(x)] is the same thing.

Answers can be left un-simplified ^_^
THANK THE LORD!!!

Example: f(x)=(x^7+3x^3+4x^2+7)(x^6+5x^4-3x)
f'(x)=(x^7+3x^3+4x^2+7)(6x^5+20x^3+3) + (x^6+5x^4-3x)(7x^6+9x^2+8x)

2. The Quotient Rule: [h'(x) = f(x) / g(x)] = [[g(x) x fā(x) ā f(x) x gā(x)] / [[g(x)]^2]
If I can get equation editor to work, I shall fix the equation above to make it look more realistic

The quotient rule is almost as simple as the product rule. If one is trying to find the derivative of the quotient of 2 different functions, finding the product of the denominator function[g(x)] and the derivative of the numerator function[f'(x)] minus the product of the numerator function[f(x)] and the derivative of the denominator function[g'(x)] all over the square of the denominator function[[g(x)]^2] is the same thing.

A good way to remember the quotient rule is the song: "Lo di-Hi minus Hi di-Lo over the square of what's down below"

Answers can be left un-simplified like the product rule ^_^
THANK THE LORD AGAIN!!!

Example: h(x)=(3x^2+e^x) / (4x^3-12x)
h'(x)=[(4x^3-12x)(6x+e^x)-(3x^2+e^x)(12x^2-12)] / [(4x^3-12x)^2]

http://tutorial.math.lamar.edu/AllBrowsers/2413/ProductQuotientRule.asp

Before I...PEACE OUT!!!(That phrase is so unlike me -_-)
Here's a picture of myself doing a chair freeze ^_^

Here's a picture of a very pretty Korean pop-star! BoA ^_^

One joke to top everything off ^_^
Q: What do you get if you add two apples and three apples?
A: A high school math problem!

And last, but not least...

At 9:02 PM,  crystal said...

hey
thats awesome. really good blog. i like the definitions.

and...nice BoA pic.
crystal

At 11:40 PM,  Ryan said...

joseph- i really liked your post. You didnt just use the definitons in the book for the product and quotient rules, but showed how they worked. i really like that

At 7:42 PM,  Ismael said...

Joseph

thanks for the good step-by-step explanations of the problems. They really helped me understand new things about the quotient rule. And, banking off of what Ryan said, you didn't just post random numbers and equations, but gafve your blog a nice human and personal effect. Good job.