Найти значение производной в точке $$x_0$$. A) $$f(x) = \frac{x^2-1}{2x+1}$$, $$x_0 = 1$$ Б) $$f(x) = (2x^2+1) (4+x^3)$$, $$x_0 = 1$$

A) $$f(x) = \frac{x^2-1}{2x+1}$$, $$x_0 = 1$$ $$f'(x) = \frac{(2x)(2x+1) - (x^2-1)(2)}{(2x+1)^2} = \frac{4x^2+2x - 2x^2+2}{(2x+1)^2} = \frac{2x^2+2x+2}{(2x+1)^2}$$ $$f'(1) = \frac{2(1)^2+2(1)+2}{(2(1)+1)^2} = \frac{2+2+2}{3^2} = \frac{6}{9} = \frac{2}{3}$$ Б) $$f(x) = (2x^2+1) (4+x^3)$$, $$x_0 = 1$$ $$f'(x) = (4x)(4+x^3) + (2x^2+1)(3x^2) = 16x + 4x^4 + 6x^4 + 3x^2 = 10x^4 + 3x^2 + 16x$$ $$f'(1) = 10(1)^4 + 3(1)^2 + 16(1) = 10+3+16 = 29$$