Module 12 - Rules of Differentiation

Module 12 - Answers

Lesson 1

Answer 1

12.1.1

When y = sin x is increasing the derivative is positive. When y = sin x is decreasing the derivative is negative.

Answer 2

12.1.2

When y = sin x has a turning point the derivative is zero.

Answer 3

12.1.3

The derivative of y = sin x is y = cos x.

Answer 4

12.1.4 The derivative of y = cos x is y = -sin x.

Answer 5

12.1.5 The amplitude of the derivative is 2 and its period is

Answer 6

12.1.6 The derivative of y = sin 2x is y ' = 2cos 2x.

Answer 7

12.1.7

The derivative of y = sin 3x is the function y = 3cos 3x. We usually write y ' = 3 cos 3x.

The derivative of y = sin 4x is y ' = 4cos 4x.

Answer 8

12.1.8 The derivative of y = sin kx is y ' = k cos kx.

Answer 9

12.1.9 The derivatives are:

Answer 10

12.1.10 The derivative of y = cos(kx) is y ' = -k sin(kx).

Answer 11

12.1.11 The graphs of Y₁ and Y₂ appear to be the same.

Answer 12

12.1.12 The derivative of y = e^x is y ' = e^x.

Answer 13

12.1.13 The derivatives are:

Answer 14

12.1.14 The derivative of y = e^kx is y' = ke^kx.

Answer 15

12.1.15 The derivative of y = f(kx) is y ' = k f '(kx).

Lesson 2

Answer 1

12.2.1

The derivative is .

Graphical support:


	[-3, 3, 1] x [-2, 2,1]

Self Test

Answer 1

Answer 2

False. A calculator can only be used to support, not prove analytic work.

Answer 3

False

Answer 4


	[-3, 3, 1] x [-2, 2, 1]

Answer 5

[-3, 3, 1] x [-5, 5, 1]