Derivatives of Exponential and
Logarithmic Functions Unit
Assignment
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! Provide full solutions, showing all of your steps.
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! Use one equal sign per line.
! Make sure that equal signs line up vertically.
! Don’t use self-developed short form notations.
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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