Verified answer

1)

[tex]f(x) = \frac{1}{3} {x}^{9} - 9 \\ f'(x) = \frac{9}{3} {x}^{9 - 1} = 3 {x}^{8} [/tex]

2)

[tex]y = - \frac{9}{x} - x \\ y' = - 9 \times ( - \frac{1}{ {x}^{2} } ) - 1x {}^{1 - 1} = \frac{9}{x {}^{2} } - 1[/tex]

3)

[tex]y = {x}^{3} - 2 {x}^{2} - 1 \\ y' = 3x {}^{3 - 1} - 2 \times 2 {x}^{2 - 1} = 3 {x}^{2} - 4x[/tex]