Tính đạo hàm của hàm số sau \[y = \frac{{2x + 1}}{{x + 2}}\]

A.\[y' = \frac{{3x}}{{\sqrt {{x^2} + 1} }}\]

B. \[y' = \frac{{9{x^2} - x + 3}}{{\sqrt {{x^2} + 1} }}\]

C. \[y' = \frac{{9{x^2} - 2x + 3}}{{\sqrt {{x^2} + 1} }}\]

D. \[y' = \frac{{6{x^2} - x + 3}}{{\sqrt {{x^2} + 1} }}\]

A.\[y' = \frac{{ - 13{x^2} - 10x + 1}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

B. \[y' = \frac{{ - 13{x^2} + 5x + 11}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

C. \[y' = \frac{{ - 13{x^2} + 5x + 1}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

D. \[y' = \frac{{ - 13{x^2} + 10x + 1}}{{{{\left( {{x^2} - 5x + 2} \right)}^2}}}\]

A.\[(uv)' = u'v + v'u\]

B. \[(u + v)' = u' + v'\]

C. \[(u - v)' = u' - v'\]

D. \[{\left( {\frac{u}{v}} \right)^\prime } = \frac{{u'v + v'u}}{{{v^2}}}\]

D. \[ - \frac{3}{2}\]

A.\[\frac{1}{6}\]

B. \[\frac{1}{{12}}\]

C. \[ - \frac{1}{6}\]

D. \[ - \frac{1}{{12}}\]

A.\[m \le \sqrt 2 \]

B. \[m \le 2\]

C. \[m \le 0\]

D. \(m < 0\)

A.\[y' = \sin x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right) + \cos x\left( {6{x^3} + 19{x^2} - 2} \right)\]

B. \[y' = \sin x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right) - \cos x\left( {6{x^3} + 19{x^2} - 2} \right)\]

C. \[y' = \sin x\left( {6{x^3} + 19{x^2} - 2} \right) + \cos x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right)\]

D. \[y' = \sin x\left( {6{x^3} + 19{x^2} - 2} \right) - \cos x\left( { - 6{x^3} + 17{x^2} + 4x - 2} \right)\]