Hàm số \(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iGacshacaGGHbGaaiOBamaaCaaaleqabaGaaGOmaaaakmaalaaa % baGaamiEaaqaaiaaikdaaaaaaa!3D85! y = {\tan ^2}\frac{x}{2}\) có đạo hàm là:
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Lời giải:
Báo sai\(% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpdaqadaqaaiGacshacaGGHbGaaiOBamaalaaabaGaamiE % aaqaaiaaikdaaaaacaGLOaGaayzkaaGaai4jaiaac6cacaaIYaGaci % iDaiaacggacaGGUbWaaSaaaeaacaWG4baabaGaaGOmaaaacqGH9aqp % daWcaaqaaiaaigdaaeaacaaIYaaaamaalaaabaGaaGymaaqaaiGaco % gacaGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakmaalaaabaGaamiE % aaqaaiaaikdaaaaaaiaaikdaciGG0bGaaiyyaiaac6gadaWcaaqaai % aadIhaaeaacaaIYaaaaiabg2da9maalaaabaGaaGymaaqaaiGacoga % caGGVbGaai4CamaaCaaaleqabaGaaGOmaaaakmaalaaabaGaamiEaa % qaaiaaikdaaaaaaiaac6cadaWcaaqaaiGacohacaGGPbGaaiOBamaa % laaabaGaamiEaaqaaiaaikdaaaaabaGaci4yaiaac+gacaGGZbWaaS % aaaeaacaWG4baabaGaaGOmaaaaaaGaeyypa0ZaaSaaaeaaciGGZbGa % aiyAaiaac6gadaWcaaqaaiaadIhaaeaacaaIYaaaaaqaaiGacogaca % GGVbGaai4CamaaCaaaleqabaGaaG4maaaakmaalaaabaGaamiEaaqa % aiaaikdaaaaaaaaa!705C! y' = \left( {\tan \frac{x}{2}} \right)'.2\tan \frac{x}{2} = \frac{1}{2}\frac{1}{{{{\cos }^2}\frac{x}{2}}}2\tan \frac{x}{2} = \frac{1}{{{{\cos }^2}\frac{x}{2}}}.\frac{{\sin \frac{x}{2}}}{{\cos \frac{x}{2}}} = \frac{{\sin \frac{x}{2}}}{{{{\cos }^3}\frac{x}{2}}}\)