Cho hàm số $% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiabg2 % da9iGacogacaGGVbGaaiiDamaaCaaaleqabaGaaGOmaaaakmaalaaa % baGaamiEaaqaaiaaisdaaaaaaa!3D8A! y = {\cot ^2}\frac{x}{4}$. Khi đó nghiệm của phương trình y’=0 là:

Ta có $% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGabmyEayaafa % Gaeyypa0ZaaeWaaeaaciGGJbGaai4BaiaacshadaahaaWcbeqaaiaa % ikdaaaGcdaWcaaqaaiaadIhaaeaacaaI0aaaaaGaayjkaiaawMcaam % aaCaaaleqabaGccWaGGBOmGikaaiabg2da9iaaikdaciGGJbGaai4B % aiaacshadaWcaaqaaiaadIhaaeaacaaI0aaaamaabmaabaGaci4yai % aac+gacaGG0bWaaSaaaeaacaWG4baabaGaaGinaaaaaiaawIcacaGL % PaaadaahaaWcbeqaaOGamai4gkdiIcaacqGH9aqpdaWcaaqaaiaaig % daaeaacaaIYaaaaiGacogacaGGVbGaaiiDamaalaaabaGaamiEaaqa % aiaaisdaaaWaaeWaaeaacaaIXaGaey4kaSIaci4yaiaac+gacaGG0b % WaaWbaaSqabeaacaaIYaaaaOWaaSaaaeaacaWG4baabaGaaGinaaaa % aiaawIcacaGLPaaaaaa!61CA! y' = {\left( {{{\cot }^2}\frac{x}{4}} \right)^\prime } = 2\cot \frac{x}{4}{\left( {\cot \frac{x}{4}} \right)^\prime } = \frac{1}{2}\cot \frac{x}{4}\left( {1 + {{\cot }^2}\frac{x}{4}} \right)$

Mà $% MathType!MTEF!2!1!+- % feaahqart1ev3aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr % 4rNCHbGeaGqiVu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq-Jc9 % vqaqpepm0xbba9pwe9Q8fs0-yqaqpepae9pg0FirpepeKkFr0xfr-x % fr-xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamyEaiaacE % cacqGH9aqpcaaIWaGaeyi1HS9aaSaaaeaacaaIXaaabaGaaGOmaaaa % ciGGJbGaai4BaiaacshadaWcaaqaaiaadIhaaeaacaaI0aaaamaabm % aabaGaaGymaiabgUcaRiGacogacaGGVbGaaiiDamaaCaaaleqabaGa % aGOmaaaakmaalaaabaGaamiEaaqaaiaaisdaaaaacaGLOaGaayzkaa % Gaeyi1HSTaci4yaiaac+gacaGG0bWaaSaaaeaacaWG4baabaGaaGin % aaaacqGH9aqpcaaIWaGaeyi1HS9aaSaaaeaacaWG4baabaGaaGinaa % aacqGH9aqpdaWcaaqaaiabec8aWbqaaiaaikdaaaGaey4kaSIaam4A % aiabec8aWjabgsDiBlaadIhacqGH9aqpcaaIYaGaeqiWdaNaey4kaS % Iaam4AaiaaisdacqaHapaCcaGGSaGaaGPaVlaaykW7caWGRbGaeyic % I4SaeSijHikaaa!716E! y' = 0 \Leftrightarrow \frac{1}{2}\cot \frac{x}{4}\left( {1 + {{\cot }^2}\frac{x}{4}} \right) \Leftrightarrow \cot \frac{x}{4} = 0 \Leftrightarrow \frac{x}{4} = \frac{\pi }{2} + k\pi \Leftrightarrow x = 2\pi + k4\pi ,\,\,k \in Z$