Question

Доказательство с применением производной. Помогите()

Answer 1

$f(x) = frac6x\f(x + Delta x) = frac{6}{x+Delta x}\Delta y = f(x + Delta x) - f(x) = frac{6}{x+ Delta x} - frac6x = frac{6x - 6x - 6Delta x}{x(x + Delta x)} = frac{-6Delta x}{x(x + Delta x)}\\frac{Delta y}{Delta x} = frac{-6}{x^2 + Delta x cdot x}\\limlimits_{Delta xto0}frac{Delta y}{Delta x} = limlimits_{Delta xto0}frac{-6}{x^2 + underbrace{Delta xcdot x}_{to0}} = -frac{6}{x^2}$