Question

Найти производные
----------------

Answer 1

y`=[(x²+1)`(x²+x+1)-(x²+x+1)`(x²+1)]/(x²+x+1)²

=[2x(x²+x+1)-2x(x²+1)]/(x²+x+1)²=(2x³+2x²+2x-2x³-2x-x²-1)/(x²+x+1)²=

=(x²-1)/(x²+x+1)²  

Answer 2

$y^{/} = \frac{2x(x^2+x+1)-(2x+1)(x^2+1)}{(x^2+x+1)^2} = \\ \frac{2x^3+2x^2+2x-2x^3-x^2-2x-1}{(x^2+x+1)^2} \\ \frac{x^2-1}{(x^2+x+ \\ 1)^2}$