Cho hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iaadAgacaGGOaGaamiEaiaacMcacqGHsislciGGJbGaai4Baiaa % cohadaahaaWcbeqaaiaaikdaaaGccaWG4baaaa!40E9! y = f(x) - {\cos ^2}x\) với f(x) là hàm liên tục trên R. Trong bốn biểu thức dưới đây, biểu thức nào xác định hàm f(x) thỏa mãn y’=1 với mọi \(x\in R\)?
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0JabmOzayaafaWaaeWaaeaacaWG4baacaGLOaGaayzkaaGa % eyOeI0IaaGOmaiaac6caciGGJbGaai4BaiaacohacaWG4bGaaiOlam % aabmaabaGaeyOeI0Iaci4CaiaacMgacaGGUbGaamiEaaGaayjkaiaa % wMcaaiabg2da9iqadAgagaqbamaabmaabaGaamiEaaGaayjkaiaawM % caaiabgUcaRiaaikdacaGGUaGaci4yaiaac+gacaGGZbGaamiEaiaa % c6caciGGZbGaaiyAaiaac6gacaWG4bGaeyypa0JabmOzayaafaWaae % WaaeaacaWG4baacaGLOaGaayzkaaGaey4kaSIaci4CaiaacMgacaGG % UbGaaGOmaiaadIhaaaa!61C9! y' = f'\left( x \right) - 2.\cos x.\left( { - \sin x} \right) = f'\left( x \right) + 2.\cos x.\sin x = f'\left( x \right) + \sin 2x\)
\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaeyO0H4Tabm % yEayaafaGaeyypa0JaaGymaiabgsDiBlqadAgagaqbamaabmaabaGa % amiEaaGaayjkaiaawMcaaiabgUcaRiGacohacaGGPbGaaiOBaiaaik % dacaWG4bGaeyypa0JaaGymaiabgsDiBlqadAgagaqbamaabmaabaGa % amiEaaGaayjkaiaawMcaaiabg2da9iaaigdacqGHsislciGGZbGaai % yAaiaac6gacaaIYaGaamiEaiabgsDiBlaadAgadaqadaqaaiaadIha % aiaawIcacaGLPaaacqGH9aqpcaWG4bGaey4kaSYaaSaaaeaacaaIXa % aabaGaaGOmaaaaciGGJbGaai4BaiaacohacaaIYaGaamiEaaaa!6406! \Rightarrow y' = 1 \Leftrightarrow f'\left( x \right) + \sin 2x = 1 \Leftrightarrow f'\left( x \right) = 1 - \sin 2x \Leftrightarrow f\left( x \right) = x + \frac{1}{2}\cos 2x\)