Section 3.4
Product and Quotient Rule
Differentiation is linear for addition, but multiplication and division require special handling.
1
The Rules
Common Pitfall:
. You cannot just multiply the derivatives!
Product Rule
For :
"Left d-Right + Right d-Left"
Quotient Rule
For :
"Lo d-Hi minus Hi d-Lo, over Lo Lo"
2
Worked Example
Find the derivative of .
Step 1: Identify Hi and Lo
- Hi: →
- Lo: →
Step 2: Apply Formula
Step 3: Simplify Numerator
3
More Examples
Product Rule
Differentiate .
Identify f and g:
Apply Formula:
Quotient Rule
Differentiate .
Identify Hi and Lo:
Apply Formula:
5
Practice Quiz
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