Question Number 96581 by Hamida last updated on 02/Jun/20
Answered by Rio Michael last updated on 03/Jun/20
$$\:{y}\:=\:\frac{\mathrm{7}{x}\:+\:\mathrm{8}}{\mathrm{8}{x}\:+\:\mathrm{2}}\: \\ $$$$\:\frac{{dy}}{{dx}}\:=\:\frac{\mathrm{7}\left(\mathrm{8}{x}\:+\:\mathrm{2}\right)−\mathrm{8}\left(\mathrm{7}{x}\:+\:\mathrm{8}\right)}{\left(\mathrm{8}{x}\:+\:\mathrm{2}\right)^{\mathrm{2}} }\:=\:−\frac{\mathrm{50}}{\left(\mathrm{8}{x}\:+\:\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$\frac{{dy}}{{dx}}\mid_{\left(\mathrm{2},\mathrm{3}\right)} =\:−\frac{\mathrm{50}}{\left(\mathrm{18}\right)^{\mathrm{2}} }\:=−\frac{\mathrm{50}}{\mathrm{324}} \\ $$$$ \\ $$