谁的导数是sin（x/2）啊 sin(x/2) 的导数是什么
\u8c01\u7684\u5bfc\u6570\u662fsin²\uff08x/2\uff09\uff1f\uff1f\uff1fsin²(x/2)=(1-cosx)/2
\u2234x/2-sinx/2+c\u7684\u5bfc\u6570\u662f
\u5bfc\u6570\u7684\u57fa\u672c\u516c\u5f0f\u3002
-2cos（x/2）
绛旓細甯哥敤鐨勪笁瑙掑嚱鏁瀵兼暟銆(sinx)'=cosx (cosx)'=-sinx (tanx)'=sec²x=1+tan²x (cotx)'=-csc²x (secx)' =tanx路secx (cscx)' =-cotx路cscx.(tanx)'=(sinx/cosx)'=[cosx路cosx-sinx路(-sinx)]/cos²x=sec²x ...
绛旓細灏sin(x+鈻硏)-sinx灞曞紑锛宻inxcos鈻硏+cosxsin鈻硏-sinx,鐢变簬鈻硏鈫0,鏁卌os鈻硏鈫1,浠庤宻inxcos鈻硏+cosxsin鈻硏-sinx鈫抍osxsin鈻硏,浜庢槸锛坰inx)鈥欙紳lim(cosxsin鈻硏)/鈻硏,鈻硏鈫0鏃讹紝lim(sin鈻硏)/鈻硏=1 鎵浠 (sinx)鈥欙紳cosx 瀵兼暟锛圖erivative锛夛紝涔熷彨瀵煎嚱鏁鍊笺傚張鍚嶅井鍟嗭紝鏄井绉垎涓殑閲...
绛旓細棣栧厛锛屾垜浠潵璁＄畻姝ｅ鸡鍑芥暟sin(x)鐨勫鏁銆傛垜浠彲浠ヤ娇鐢ㄦ瀬闄愮殑瀹氫箟鏉ユ帹瀵煎嚭瀹冪殑瀵兼暟锛歞/dx sin(x) = lim(h->0) [sin(x+h) - sin(x)] / h 鏍规嵁涓夎鍑芥暟鐨勫拰宸叕寮忥紝鎴戜滑鍙互灞曞紑鍒嗗瓙锛=lim(h->0) [sin(x)cos(h) + cos(x)sin(h) - sin(x)] / h 鍐嶅埄鐢ㄦ瀬闄愮殑鎬ц川鍖栫畝锛=lim(...
绛旓細姝ｅ鸡鍑芥暟 sin(x)鐨勫鏁版槸浣欏鸡 cos(x)銆倅 = f(x) = sin(x)dy/dx =lim[f(x+螖x)-f(x)]/螖x 螖x鈫0 =lim[sin(x+螖x)-sin(x)]/螖x 螖x鈫0 =lim{2cos[(2x+螖x)/2]sin[(x+螖x-x)/2]}/螖x 螖x鈫0 =lim2[cos(x+螖x/2)sin(螖x/2]/螖x 螖x鈫0 =lim[cos...
绛旓細锛1锛墆=sinx鐨勫鏁帮細y鈥=cosx 锛2锛墆=cosx鐨勫鏁帮細y鈥=-sinx 涓句緥濡備笅锛氾紙1锛(sin3x)'=3cos3x 锛2锛(sin5x)'=5cos5x 锛3锛(cos3x)'=-3sin3x 锛4锛(cos5x)'=-5sin5x sinX鏄寮﹀嚱鏁帮紝鑰宑osX鏄綑寮﹀嚱鏁帮紝涓よ呭鏁颁笉鍚岋紝sinX鐨勫鏁版槸cosX锛岃宑osX鐨勫鏁版槸 -sinX锛岃繖鏄洜涓轰袱涓...
绛旓細鏄剧劧(sinx)鈥欙紳cosx锛屽畾涔夋眰瑙:渚涘弬鑰冿紝璇风瑧绾炽傚叾涓娇鐢ㄥ埌涓夎鍑芥暟鐨勫拰宸寲绉叕寮忋傞珮涓暟瀛︿腑琚垹闄や簡锛岄珮绛夋暟瀛︿緷鐒堕渶瑕佷娇鐢ㄣ
绛旓細涓汉鎰熻杩欎釜鏄嚜宸辨兂鍑烘潵鐨勫紡瀛愶紝鏍规湰灏辨病鏈夎繖绉嶈〃绀烘柟娉曪紝杩欎篃涓嶆槸澶嶅悎鍑芥暟姹傚锛屾嫭鍙锋槸涓嶅簲璇ュ瓨鍦ㄧ殑锛岃嫢y=sin锛坸锛夛紝鍒欏彲姹傚緱x=arcsiny. 鍙坹=sinx锛屽悓鏍峰緱鍒皒=arcsiny. 鍙帹寰楋紙x锛=x锛屽叾瀹炲氨鏄痽=sinx锛瀵兼暟y'=cosx
绛旓細=Sin^2(x)/Cos^2(x)=[sin(x)/cos(x)]^2 =tan^2(x)涓夎鍑芥暟鍏紡 涓よ鍜屽叕寮 sin(A+B)=sinAcosB+cosAsinB sin(A-B)=sinAcosB-sinBcosA cos(A+B)=cosAcosB-sinAsinB cos(A-B)=cosAcosB+sinAsinB tan(A+B)=(tanA+tanB)/(1-tanAtanB)tan(A-B)=(tanA-tanB)/(1+tanAtanB)ct...
绛旓細鍥犱负瀹冪殑鏋侀檺瓒嬩簬1锛屽湪楂樼瓑鏁板涔︿笂鏈夆樹袱涓噸瑕佺殑鏋侀檺鈥欒繖涓鑺傦紝鍏朵腑绗竴涓噸瑕佺殑鏋侀檺灏变负褰搙瓒嬩簬0鏃讹紝sinx/x=1,sinx涓巟浜掍负绛変环鏃犵┓灏忛噺锛屽湪姹傜Н寮忕殑鏋侀檺杩囩▼涓紝浜岃呭彲浜掔浉鏇挎崲锛涚浜屼釜閲嶈鏋侀檺鍗充负褰搙瓒嬩簬鏃犵┓澶ф椂锛(1+1/x)^x=e.鎴戞槸鏁板绯诲ぇ涓夊鐢燂紝绁濅綘濂借繍锛丟ood luck with you!
绛旓細y = sin(x) + 3鐨勫鏁版槸y' = cos(x)銆傚浣犳墍瑙侊紝杩欎袱涓鏁伴兘鏄痗os(x)锛屽畠浠槸鐩稿悓鐨勩傝繖鏄洜涓篶os(x)鏄痵in(x)鐨勫鏁帮紝鑰屽皢涓涓父鏁帮紙+3锛夋坊鍔犲埌鍑芥暟涓笉浼氭敼鍙樺鏁般傛墍浠ワ紝閫氳繃鍥惧舰鍜屽鏁扮殑鍒嗘瀽锛屾垜浠彲浠ュ緱鍑虹粨璁猴紝y = sin(x)鍜寉 = sin(x) + 3鐨勫鏁版槸鐩稿悓鐨勶紝鍥犱负瀹冧滑鍙湪y...
