Cho hàm số $% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiiOaiaadA % gadaqadaqaaiaadIhaaiaawIcacaGLPaaacqGH9aqpdaWcaaqaaiaa % iodacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGOmaiaadI % hacqGHRaWkcaaIXaaabaGaaGOmamaakaaabaGaaG4maiaadIhadaah % aaWcbeqaaiaaiodaaaGccqGHRaWkcaaIYaGaamiEamaaCaaaleqaba % GaaGOmaaaakiabgUcaRiaaigdaaSqabaaaaaaa!4B34! \;f\left( x \right) = \frac{{3{x^2} + 2x + 1}}{{2\sqrt {3{x^3} + 2{x^2} + 1} }}$. Giá trị f’(0)là:

$% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiiOaiqadA % gagaqbamaabmaabaGaaGimaaGaayjkaiaawMcaaiabg2da9maalaaa % baWaaeWaaeaacaaIZaGaamiEamaaCaaaleqabaGaaGOmaaaakiabgU % caRiaaikdacaWG4bGaey4kaSIaaGymaaGaayjkaiaawMcaamaaCaaa % leqabaGccWaGGBOmGikaaiaac6cacaaIYaWaaOaaaeaacaaIZaGaam % iEamaaCaaaleqabaGaaG4maaaakiabgUcaRiaaikdacaWG4bWaaWba % aSqabeaacaaIYaaaaOGaey4kaSIaaGymaaWcbeaakiabgkHiTmaabm % aabaGaaG4maiaadIhadaahaaWcbeqaaiaaikdaaaGccqGHRaWkcaaI % YaGaamiEaiabgUcaRiaaigdaaiaawIcacaGLPaaacaGGUaWaaeWaae % aacaaIYaWaaOaaaeaacaaIZaGaamiEamaaCaaaleqabaGaaG4maaaa % kiabgUcaRiaaikdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaS % IaaGymaaWcbeaaaOGaayjkaiaawMcaamaaCaaaleqabaGccWaGGBOm % GikaaaqaamaabmaabaGaaGOmamaakaaabaGaaG4maiaadIhadaahaa % WcbeqaaiaaiodaaaGccqGHRaWkcaaIYaGaamiEamaaCaaaleqabaGa % aGOmaaaakiabgUcaRiaaigdaaSqabaaakiaawIcacaGLPaaadaahaa % Wcbeqaaiaaikdaaaaaaaaa!72FB! \;f'\left( 0 \right) = \frac{{{{\left( {3{x^2} + 2x + 1} \right)}^\prime }.2\sqrt {3{x^3} + 2{x^2} + 1} - \left( {3{x^2} + 2x + 1} \right).{{\left( {2\sqrt {3{x^3} + 2{x^2} + 1} } \right)}^\prime }}}{{{{\left( {2\sqrt {3{x^3} + 2{x^2} + 1} } \right)}^2}}}$

$% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyypa0ZaaS % aaaeaadaqadaqaaiaaiAdacaWG4bGaey4kaSIaaGOmaaGaayjkaiaa % wMcaaiaaikdadaGcaaqaaiaaiodacaWG4bWaaWbaaSqabeaacaaIZa % aaaOGaey4kaSIaaGOmaiaadIhadaahaaWcbeqaaiaaikdaaaGccqGH % RaWkcaaIXaaaleqaaOGaeyOeI0YaaeWaaeaacaaIZaGaamiEamaaCa % aaleqabaGaaGOmaaaakiabgUcaRiaaikdacaWG4bGaey4kaSIaaGym % aaGaayjkaiaawMcaamaalaaabaGaaGyoaiaadIhadaahaaWcbeqaai % aaikdaaaGccqGHRaWkcaaI0aGaamiEaaqaamaakaaabaGaaG4maiaa % dIhadaahaaWcbeqaaiaaiodaaaGccqGHRaWkcaaIYaGaamiEamaaCa % aaleqabaGaaGOmaaaakiabgUcaRiaaigdaaSqabaaaaaGcbaWaaeWa % aeaacaaIYaWaaOaaaeaacaaIZaGaamiEamaaCaaaleqabaGaaG4maa % aakiabgUcaRiaaikdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4k % aSIaaGymaaWcbeaaaOGaayjkaiaawMcaamaaCaaaleqabaGaaGOmaa % aaaaGccqGH9aqpdaWcaaqaaiaaiMdacaWG4bWaaWbaaSqabeaacaaI % 0aaaaOGaey4kaSIaaGOnaiaadIhadaahaaWcbeqaaiaaiodaaaGccq % GHsislcaaI5aGaamiEamaaCaaaleqabaGaaGOmaaaakiabgUcaRiaa % iIdacaWG4bGaey4kaSIaaGinaaqaaiaaisdadaqadaqaaiaaiodaca % WG4bWaaWbaaSqabeaacaaIZaaaaOGaey4kaSIaaGOmaiaadIhadaah % aaWcbeqaaiaaikdaaaGccqGHRaWkcaaIXaaacaGLOaGaayzkaaWaaO % aaaeaacaaIZaGaamiEamaaCaaaleqabaGaaG4maaaakiabgUcaRiaa % ikdacaWG4bWaaWbaaSqabeaacaaIYaaaaOGaey4kaSIaaGymaaWcbe % aaaaaaaa!87EA! = \frac{{\left( {6x + 2} \right)2\sqrt {3{x^3} + 2{x^2} + 1} - \left( {3{x^2} + 2x + 1} \right)\frac{{9{x^2} + 4x}}{{\sqrt {3{x^3} + 2{x^2} + 1} }}}}{{{{\left( {2\sqrt {3{x^3} + 2{x^2} + 1} } \right)}^2}}} = \frac{{9{x^4} + 6{x^3} - 9{x^2} + 8x + 4}}{{4\left( {3{x^3} + 2{x^2} + 1} \right)\sqrt {3{x^3} + 2{x^2} + 1} }}$

$% MathType!MTEF!2!1!+- % feaahqart1ev3aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaaiiOaiqadA % gagaqbamaabmaabaGaaGimaaGaayjkaiaawMcaaiabg2da9maalaaa % baGaaGinaaqaaiaaiIdaaaGaeyypa0ZaaSaaaeaacaaIXaaabaGaaG % OmaaaacaGGUaaaaa!4026! \;f'\left( 0 \right) = \frac{4}{8} = \frac{1}{2}.$