Mathematical Methods — Question 11

QCAA 2020, Paper 1 · 3 marks

Q11 · 2020 · Technology-freeSimple familiar3 marks

QUESTION 11 (3 marks)

Determine the derivative of each of the following with respect to

x

y=\frac{1}{\sin(x)}

[1 mark]

y=x^2e^{-x}

. Express your answer in factorised form.

[2 marks]

WORKED SOLUTION

3 marks

ANSWER

-\dfrac{\cos x}{(\sin x)^2}

; b)

xe^{-x}(-x+2)

Worked solution

f'(x)=-\frac{\cos x}{(\sin x)^2}.

f'(x)=-x^2e^{-x}+2xe^{-x}=xe^{-x}(-x+2).

correctly determines the derivative

[1 mark]

correctly determines the derivative in expanded form

[1 mark]

determines factorised form of derivative

[1 mark]

One QCAA sample method typeset for web; criterion wording is adapted from the official marking guide.

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