Question

Найти производную f(x)=x^2-6x/x+2

Answer 1

$f(x)=\frac{x^2-6x}{x+2}=\frac{x^2+2x-8x}{x+2}=\frac{x^2+2x}{x+2}-\frac{8x}{x+2}=x-\frac{8x}{x+2}\\\\ f'(x)=1-8*\frac{(x)'*(x+2)-x*(x+2)'}{(x+2)^2}=1-8*\frac{1*(x+2)-x*1}{(x+2)^2}=1-\frac{16}{(x+2)^2}$