Найти производную функции y=(x²+1) /(x-1)
При x=2

ответ: -1
Объяснение:
y = (x^2 + 1) / (x-1)
f ` (x) = ((x^2 + 1) / (x-1)) ` = (x^2+1) ` × (x-1) - (x^2 + 1) × (x-1) ` / (x-1)^2 = 2x × (x-1) - (x^2 + 1) × 1 / (x-1)^2 = 2x^2 - 2x - x^2 - 1 / (x-1)^2 = x^2 - 2x - 1 / (x-1)^2
f ` (2) = 2^2 - 2 × 2 - 1 / (2-1)^2 = -1/1 = -1