Quantitative Modelling 1
DSC1520
Department of Decision Sciences
Assignment 02 for 2021 (compulsory)
Due Date: 25 June 2021
Unique Number: 387523
Instructions
• Work through chapters 4, 5 and 6 in the study guide before attempting this assignment.
• Answer all the questions.
• Submit your answers electronically through myUnisa.
Question 1
Find the derivative of
𝑦 = ln 3𝑥 5
[1] ln 3𝑥 5
[2] 15𝑥 4
[3] 5𝑥 −1
1
[4] 3𝑥 5
Answer:
The formula for the slope of the curve
𝑦 = 𝑓(𝑥) is known as the derivative of the curve with respect to 𝑥.
𝑦 = ln 3𝑥 5
𝑑𝑦 1 𝑑
= × (3𝑥 5 )
𝑑𝑥 3𝑥 5 𝑑𝑥
15𝑥 4
3𝑥 5
5𝑥 −1
, OR:
𝑦 = ln 3𝑥 5
𝑑
[𝑙𝑛3𝑥 5 ]
𝑑𝑥
1 𝑑
× [3𝑥 5 ]
3𝑥 5 𝑑𝑥
𝑑
3× [3𝑥 5 ]
𝑑𝑥
3𝑥 5
5𝑥 4
𝑥5
5
𝑥
= 5𝑥 −1
DSC1520
Department of Decision Sciences
Assignment 02 for 2021 (compulsory)
Due Date: 25 June 2021
Unique Number: 387523
Instructions
• Work through chapters 4, 5 and 6 in the study guide before attempting this assignment.
• Answer all the questions.
• Submit your answers electronically through myUnisa.
Question 1
Find the derivative of
𝑦 = ln 3𝑥 5
[1] ln 3𝑥 5
[2] 15𝑥 4
[3] 5𝑥 −1
1
[4] 3𝑥 5
Answer:
The formula for the slope of the curve
𝑦 = 𝑓(𝑥) is known as the derivative of the curve with respect to 𝑥.
𝑦 = ln 3𝑥 5
𝑑𝑦 1 𝑑
= × (3𝑥 5 )
𝑑𝑥 3𝑥 5 𝑑𝑥
15𝑥 4
3𝑥 5
5𝑥 −1
, OR:
𝑦 = ln 3𝑥 5
𝑑
[𝑙𝑛3𝑥 5 ]
𝑑𝑥
1 𝑑
× [3𝑥 5 ]
3𝑥 5 𝑑𝑥
𝑑
3× [3𝑥 5 ]
𝑑𝑥
3𝑥 5
5𝑥 4
𝑥5
5
𝑥
= 5𝑥 −1
