Question

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Решите пожалуйста, очень нужно!

Answer 1

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

Answer 2

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