Question

(x+1).(√x^{2_{+x+1 )}}

Answer 1

giúp mình vs ạ

Answer 2

Đề yêu cầu điều gì em?

Answer 3

\(y=\left(x+1\right)\sqrt{x^2+x+1}\)

\(y'=\left(x+1\right)'\sqrt{x^2+x+1}+\left(x+1\right).\left(\sqrt{x^2+x+1}\right)'\)

\(=\sqrt{x^2+x+1}+\dfrac{\left(x+1\right).\left(x^2+x+1\right)'}{2\sqrt{x^2+x+1}}\)

\(=\sqrt{x^2+x+1}+\dfrac{\left(x+1\right)\left(2x+1\right)}{2\sqrt{x^2+x+1}}\)

\(=\dfrac{2\left(x^2+x+1\right)+\left(x+1\right)\left(2x+1\right)}{2\sqrt{x^2+x+1}}\)

\(=\dfrac{4x^2+5x+3}{2\sqrt{x^2+x+1}}\)