Найдите производную функции: 9) y=(\frac{1}{x}+1)·(2x-3)

9) $y = (\frac{1}{x} + 1)(2x - 3)$ $y' = (\frac{1}{x} + 1)'(2x - 3) + (\frac{1}{x} + 1)(2x - 3)' = (-\frac{1}{x^2})(2x - 3) + (\frac{1}{x} + 1)(2) = -\frac{2x}{x^2} + \frac{3}{x^2} + \frac{2}{x} + 2 = -\frac{2}{x} + \frac{3}{x^2} + \frac{2}{x} + 2 = \frac{3}{x^2} + 2$ Ответ: $y' = \frac{3}{x^2} + 2$