Chapter 3 - Differentiation - 3.3 Product and Quotient Rules - Exercises - Page 121: 8

$ f’(x) =-\frac{x^{2}+8x+3}{(x^{2}+x+1)^{2}} $

$Quotient$ $Rule:$ $ (\frac{f}{g})’ = \frac{gf’-fg’}{g^{2}} $ $ f(x) = \frac{x+4}{x^{2}+x+1} $ $ f’(x) = \frac{(x^{2} +x+1)(1)-(x+4)(2x+1)}{(x^{2}+x+1)^{2}} $ $ f’(x) =\frac{-x^{2}-8x-3}{(x^{2}+x+1)^{2}} $