AP Physics                                                                               Please do not write on this worksheet.

Derivative Worksheet                                                               Show your work in your notebook.

 

Before you begin, carefully read "B.6 Differential Calculus"  Pg. A.19 – A.21

 

1.  a) What is a derivative?  b) How is a derivative defined mathematically?

 

2.  When the derivative is used in kinematics we seek to understand how the position or velocity of an object is changing with time.  Therefore we will be taking derivatives with respect to time, t.  Rewrite the table of derivatives (Table B.4 Pg. A.21) using "t" for time in place of the "x."

 

For the equations below a) determine the derivative, and b) evaluate the derivative when t = 3.

 

3.  x = 5t²                                                                     9.  x = 6/t²

 

4.  x = 3t³ + 4                                                               10.  x = 5t⁷ + 12/t³

 

5.  x = 4t⁵ +  6t³ + 6t                                                    11.  x = 9t⁵ + 8t⁴ + 7t³

 

6.  x = 8 cos(4t)                                                           12.  x = 4 ln(3t)

 

7.  x = 6t + 3sin(t)                                                        13.  x = 6 e^4t

 

8.  x = 12 tan(-3t)                                                         14.  x = 4t^-3  + 4 sin(6t)