Question

Найдите производную функции y=(1/x+8)(5x-2)

Answer 1

$y'=( \frac{1}{x} +8)'(5x-2)+( \frac{1}{x} +8)(5x-2)'=- \frac{1}{x^2} (5x-2)+5( \frac{1}{x} +8)=$$\frac{2-5x}{x^2} + \frac{5}{x} +40= \frac{2-5x+5x+40x^2}{x^2} = \frac{40x^2+2}{x^2}$