II. QUOTIENT RULE

D1. Differentiation Rules Continued

I. PRODUCT RULE

Recall that if , then .

But what if ?

Is ?

Consider the function, .

Method 1: Test if is correct:

Let and

Method 2: Simplify the function and use the rules from last class to find the derivative.

Do we get the same result?

The Product Rule

If and are two functions of and then

or

Ex.1. Find the derivative of the following. Simplify your result.

a. b.

Ex.2. Find the derivative of the following. Simplify your result.

a. b.

II. QUOTIENT RULE

What if we have ?

Is ?

Consider the function, .

Method 1: Test if is correct: Method 2: Use the product rule.

Let and Let and

Do we get the same result?

The Quotient Rule

So if then and

Ex.3. Find the derivative of the following. Simplify your result.

a. b.

Ex.4. Find the derivative of the following. Simplify your result.

a. b.

HOMEWORK:

Ex.2.4 #[1-3]ace, 5,6 Ex.2.5 #[1-3]ace, 4

ANSWERS:

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