Question

Find the derivative of f(x) = 8 divided by x at x = -1. 4 0 8 -8

Answer 1

$\bf \stackrel{f(x)}{y}=\cfrac{8}{x}\implies y=8x^{-1}\implies \cfrac{dy}{dx}=8(-1)x^{-2}\implies \cfrac{dy}{dx}=-8x^{-2} \\\\\\ \left. \cfrac{dy}{dx}=-\cfrac{8}{x^2}\right|_{x=-1}\implies \cfrac{-8}{(-1)^2}\implies -8$