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Date None Specimen Marks available 4 Reference code SPNone.1.sl.TZ0.7
Level SL only Paper 1 Time zone TZ0
Command term Find Question number 7 Adapted from N/A

Question

Given that \(f(x) = \frac{1}{x}\) , answer the following.

Find the first four derivatives of \(f(x)\) .

[4]
a.

Write an expression for \({f^{(n)}}(x)\) in terms of x and n .

[3]
b.

Markscheme

\(f'(x) = - {x^{ - 2}}\) (or \( - \frac{1}{{{x^2}}}\) )     A1     N1

\(f''(x) = 2{x^{ - 3}}\) (or \(\frac{2}{{{x^3}}}\) )     A1     N1

\(f'''(x) = - 6{x^{ - 4}}\) (or \( - \frac{6}{{{x^4}}}\) )     A1     N1

\({f^{(4)}}(x) = 24{x^{ - 5}}\) (or \(\frac{{24}}{{{x^5}}}\) )     A1     N1

[4 marks]

a.

\({f^{(n)}}(x) = \frac{{{{( - 1)}^n}n!}}{{{x^{n + 1}}}}\) or \({( - 1)^n}n!({x^{ - (n + 1)}})\)     A1A1A1     N3

[3 marks]

b.

Examiners report

[N/A]
a.
[N/A]
b.

Syllabus sections

Topic 6 - Calculus » 6.2 » Derivative of \({x^n}\left( {n \in \mathbb{Q}} \right)\) , \(\sin x\) , \(\cos x\) , \(\tan x\) , \({{\text{e}}^x}\) and \(\ln x\) .
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