Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iaadAgadaqadaqaaiaadIhaaiaawIcacaGLPaaacqGH9aqpciGG % ZbGaaiyAaiaac6gadaGcaaqaaiaadIhaaSqabaGccqGHRaWkciGGJb % Gaai4BaiaacohadaGcaaqaaiaadIhaaSqabaaaaa!4536! y = f\left( x \right) = \sin \sqrt x + \cos \sqrt x \). Giá trị \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cadaqadaqaamaalaaabaGaeqiWda3aaWbaaSqabeaacaaIYaaaaaGc % baGaaGymaiaaiAdaaaaacaGLOaGaayzkaaaaaa!3D4E! f'\left( {\frac{{{\pi ^2}}}{{16}}} \right)\) bằng:
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cadaqadaqaaiaadIhaaiaawIcacaGLPaaacqGH9aqpdaWcaaqaaiaa % igdaaeaacaaIYaWaaOaaaeaacaWG4baaleqaaaaakiGacogacaGGVb % Gaai4CamaakaaabaGaamiEaaWcbeaakiabgkHiTmaalaaabaGaaGym % aaqaaiaaikdadaGcaaqaaiaadIhaaSqabaaaaOGaci4CaiaacMgaca % GGUbWaaOaaaeaacaWG4baaleqaaOGaeyypa0ZaaSaaaeaacaaIXaaa % baGaaGOmamaakaaabaGaamiEaaWcbeaaaaGcdaqadaqaaiGacogaca % GGVbGaai4CamaakaaabaGaamiEaaWcbeaakiabgkHiTiGacohacaGG % PbGaaiOBamaakaaabaGaamiEaaWcbeaaaOGaayjkaiaawMcaaaaa!5758! f'\left( x \right) = \frac{1}{{2\sqrt x }}\cos \sqrt x - \frac{1}{{2\sqrt x }}\sin \sqrt x = \frac{1}{{2\sqrt x }}\left( {\cos \sqrt x - \sin \sqrt x } \right)\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamOzaiaacE % cadaqadaqaamaalaaabaGaeqiWda3aaWbaaSqabeaacaaIYaaaaaGc % baGaaGymaiaaiAdaaaaacaGLOaGaayzkaaGaeyypa0ZaaSaaaeaaca % aIXaaabaGaaGOmamaakaaabaWaaeWaaeaadaWcaaqaaiabec8aWbqa % aiaaisdaaaaacaGLOaGaayzkaaWaaWbaaSqabeaacaaIYaaaaaqaba % aaaOWaaeWaaeaaciGGJbGaai4BaiaacohadaGcaaqaamaabmaabaWa % aSaaaeaacqaHapaCaeaacaaI0aaaaaGaayjkaiaawMcaamaaCaaale % qabaGaaGOmaaaaaeqaaOGaeyOeI0Iaci4CaiaacMgacaGGUbWaaOaa % aeaadaqadaqaamaalaaabaGaeqiWdahabaGaaGinaaaaaiaawIcaca % GLPaaadaahaaWcbeqaaiaaikdaaaaabeaaaOGaayjkaiaawMcaaiab % g2da9maalaaabaGaaGymaaqaaiaaikdacaGGUaWaaSaaaeaadaGcaa % qaaiaaikdaaSqabaaakeaacaaIYaaaaaaadaqadaqaamaalaaabaWa % aOaaaeaacaaIYaaaleqaaaGcbaGaaGOmaaaacqGHsisldaWcaaqaam % aakaaabaGaaGOmaaWcbeaaaOqaaiaaikdaaaaacaGLOaGaayzkaaGa % eyypa0JaaGimaaaa!63BD! f'\left( {\frac{{{\pi ^2}}}{{16}}} \right) = \frac{1}{{2\sqrt {{{\left( {\frac{\pi }{4}} \right)}^2}} }}\left( {\cos \sqrt {{{\left( {\frac{\pi }{4}} \right)}^2}} - \sin \sqrt {{{\left( {\frac{\pi }{4}} \right)}^2}} } \right) = \frac{1}{{2.\frac{{\sqrt 2 }}{2}}}\left( {\frac{{\sqrt 2 }}{2} - \frac{{\sqrt 2 }}{2}} \right) = 0\)