Dsc1520 assignment 3 verified 2025 new

DSC1520 ASSIGNMENT 3
POSSIBLE SOLUTIONS


Question 1
Find the derivative of the function:

Replace with , expand the brackets and simplify before differentiating




Apply the “Power Rule” of differentiation.

If then

Also, if then

Note: The derivative of is and the derivative of a constant term is .




Replace with

,Question 2
Differentiate the function




Apply the “Quotient rule” of differentiation.

Let
and




Factor out 2, the common factor on the numerator




Now, factorize the bracket on the numerator




Page 2

, DSC1520 ASSIGNMENT 3
POSSIBLE SOLUTIONS
Question 3
Find the derivative of the function




Apply the “Product rule” on and “Quotient rule” on


Let where




where
and

[Product rule]




where
and