1 of 24

Grade 12

Mathematics

​

​

2 of 24

Online Classroom Rules

3 of 24

4 of 24

Find the derivative of a function at a given point using the Power Rule

Learning Objectives

Sketch the graph of a function using the graph of its derivative

Use differentiation rules and higher derivatives in solving real-life problems

5 of 24

6 of 24

7 of 24

8 of 24

9 of 24

10 of 24

11 of 24

12 of 24

13 of 24

14 of 24

First derivative

​

​

Second derivative

​

​

Third derivative

​

​

Fourth derivative

​

​

Fifth derivative

Note: For fourth and higher derivatives, we indicate the order of the derivative in parentheses.

Be careful to distinguish these from exponents.

15 of 24

16 of 24

You are probably familiar with the term acceleration, which is the instantaneous rate of change of velocity.

​

Consequently, if the velocity of an object at time t is given by v(t), then the acceleration is

17 of 24

18 of 24

19 of 24

20 of 24

21 of 24

22 of 24

23 of 24

24 of 24