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

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

$f'(x) = - {x^{ - 2}}$ (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]

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

[3 marks]