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Mat1512 Assignment 3 Solutions 2026

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Mat1512 Assignment 3 Solutions 2026 0-7-9-3-2-2-6-4-2-7 UNISA University of South Africa College of Science, Engineering and Technology Department of Mathematical Sciences Tutorial Letter 103/3/2026 MAT1512 – Calculus I Assignment 03 Opened: Thursday, 1 January 2026, 8:00 AM Due: Monday, 27 July 2026, 8:00 PM

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Institution
University Of South Africa (Unisa)
Course
Calculus A (MAT1512)

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Mat1512 Assignment 3 Solutions 2026
UNISA
University of South Africa College of Science,
Engineering and Technology Department of
Mathematical Sciences Tutorial Letter 103/3/2026
MAT1512 – Calculus I Assignment 03
Opened: Thursday, 1 January 2026, 8:00 AM
Due: Monday, 27 July 2026, 8:00 PM

, QUESTION 1

Differentiate the following.

(a) 𝒚 = 𝒙𝟑 𝐥𝐧⁡ 𝒙(4 Marks)

Identify the rule

Since there are two functions multiplied together,

𝑢 = 𝑥 3 , 𝑣 = ln⁡ 𝑥


Use the Product Rule
𝑑𝑦
= 𝑢′ 𝑣 + 𝑢𝑣 ′
𝑑𝑥


Differentiate each function

Differentiate 𝑥 3 :

𝑢′ = 3𝑥 2


Differentiate ln 𝑥:
1
𝑣′ =
𝑥
Substitute into the Product Rule
𝑑𝑦 1
= (3𝑥 2 )(ln⁡ 𝑥) + (𝑥 3 ) ( )
𝑑𝑥 𝑥


Step 4: Simplify

Since
1
𝑥3 ( ) = 𝑥2,
𝑥


then

𝑑𝑦
= 3𝑥 2 ln⁡ 𝑥 + 𝑥 2
𝑑𝑥


𝑑𝑦
= 𝑥 2 (3ln⁡ 𝑥 + 1)
𝑑𝑥
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