SM015 - 9.2 (Notes Solutions)

9.2 Rules of Differentiation

Learning Outcomes:
At the end of the lesson, students should be able to
(a) Apply the rules of differentiation.
(b) Perform second and third order differentiation.



Rules of Differentiation

1. Basic Differentiation
•
•
2. Sum and Difference Rule
•

3. Product Rule
•

4. Quotient Rule
•

5. Chain Rule •
• •

6. Power Rule
•

Topic 9.2 Page 1

Rules of Differentiation ( Part I )

Sunday, June 21, 2020 3:12 PM

1. Basic Differentiation
•

•

Example 1: with respect to x.
Differentiate
Solution:

Example 2:
Differentiate the following with respect to x.

Solution: Solution:

2. Sum and Difference Rule with respect to x.
•

Example 3:
Find the derivative of
Solution:

Topic 9.2 Page 2

Rules of Differentiation ( Part II )

Sunday, June 21, 2020 3:12 PM

3. Product Rule
•

Example 4: with respect to x by using product rule.
Differentiate
Solution:

4. Quotient Rule
•

Example 5: with respect to x by using quotient rule.
Differentiate

Solution:

Topic 9.2 Page 3

Rules of Differentiation ( Part III )

Sunday, June 21, 2020 3:12 PM

5. Chain Rule
•

Example 6: for
By using Chain Rule, find ,

Solution:

6. Power Rule with respect to x .
•

Example 7:
Differentiate
Solution:

Topic 9.2 Page 4

Higher Order Derivatives

Sunday, June 21, 2020 3:12 PM

For the function , the corrseponding derivatives are denotes as:

Derivative

Derivative

Derivative

Derivative

Derivative
Remarks:

Example 8:

Find the third derivatives with respect to x for

Solution:

Topic 9.2 Page 5