Найдите производную ф-ции f(x) = [latex]\frac{ x^{2} + x+1 }{x^{2} +1} [/latex]

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