## Derivatives of Exponential and Logarithmic Functions Unit

Derivatives of Exponential and

Logarithmic Functions Unit

Assignment

You may choose to complete your mathematical calculations by hand and scan or

take images to upload to the dropbox. To help your teacher review your work,

please try to submit your calculations as a single file document (preferably as a

pdf). If you aren’t sure how to do this, please contact your teacher for assistance.

Important

When answering questions in a mathematics course always be sure to use

the following guidelines to help you do your best:

! Provide full solutions, showing all of your steps.

! Make sure that there is one step or idea per line.

! Use one equal sign per line.

! Make sure that equal signs line up vertically.

! Don’t use self-developed short form notations.

# ” Listen !

Derivatives of Exponential and Logarithmic Functions Unit Assignment 2022-10-17, 9:30 PM

https://lms.virtualhighschool.com/content/vhs3/departments/mat/c…d2lSessionVal=TbEghofnVPdbdngswTdLusNwB&ou=64461&d2l_body_type=3 Page 2 of 3

Note that derivatives must be fully simplified for full marks on this Note that derivatives must be fully simplified for full marks on this

assignment. assignment.

1. Find the derivatives of each of these functions: (2 marks each) marks each)

a. y = ln(4×2 + 4)

b. y = 2x

4

e5x

c. y = 25x+7(ln(5x + 1))

d. y = 4x

3

e5x+x4

2. Use the process of implicit differentiation to find given that

.

dy

dx

x3ey − yex = 0

(4 marks) (4 marks)

3. Use curve sketching methods, sketch the graph of the function given by the

equation . Make sure that you include all steps, charts, and derivations

details.

y = x

2

ex

(10 marks)

4. Use logarithmic differentiation to find the derivative of the function

y = . (2x+5)

3

(5x

2

−2x)

4

√2x+5 (6 marks)

5. The population, , of an island, years after colonization is given by the

function .

P y

P = 250

1+4e−0.01y

a. What was the initial population of the island? (2 marks)

b. How long did it take before the island had a population of 150? (2 marks)

c. After how many years was the population growing the fastest? (3 marks)

d. Using curve sketching methods, sketch the graph of the function. Make

sure that you include all steps, charts, and derivations details. (10 marks) (10 marks)

e. Give a possible explanation for the shape of the curve. (3 marks)

Derivatives of Exponential and Logarithmic Functions Unit Assignment 2022-10-17, 9:30 PM

https://lms.virtualhighschool.com/content/vhs3/departments/mat/c…d2lSessionVal