Question

Suppose that f(x)=2/x^9. Evaluate each of the following:

f′(2) =

f′(−3) =

Answer 1

$\displaystyle f(x) = \frac{2}{x^9} = 2x^{-9}\\ f'(x) = -18x^{-10}\\ f'(2) = -18\times 2^{-10} = \frac{-9}{512}\\ f'(-3) = -18\times (-3)^{-10} = \frac{-2}{3^8} = \frac{-2}{6561}$