sin2x的导数是 sin2x的导函数是什么，为什么。
sin2x\u5bfc\u6570\u662f\u4ec0\u4e48\uff1fSinX\u7684\u5bfc\u6570\u662fCosX
\u590d\u5408\u51fd\u6570\u516c\u5f0fY'x=Y'u*Ux'
\u5148\u628a2x\u770b\u505a\u4e00\u4e2a\u6574\u4f53u
\u5148\u6c42\u51fasinu\u7684\u5bfc\u6570
\u7136\u540e\u5728\u5bf92x\u6c42\u5bfc
\u6700\u540e\u7ed3\u679c
=(2x)'*(sinu)'
=2cos2x
SinX\u7684\u5bfc\u6570\u662fCosX
\u590d\u5408\u51fd\u6570\u516c\u5f0fY'x=Y'u*Ux'
\u5148\u628a2x\u770b\u505a\u4e00\u4e2a\u6574\u4f53u
\u5148\u6c42\u51fasinu\u7684\u5bfc\u6570
\u7136\u540e\u5728\u5bf92x\u6c42\u5bfc
\u6700\u540e\u7ed3\u679c
=(2x)'*(sinu)'
=2cos2x
y'=cos2x(2x)'=2cos2x.即(sin2x)'=2cos2x.
y'=cos2x(2x)'=2cos2x.
(sin2x)'=2cos2x
绛旓細sin2x鐨勫鏁帮細2cos2x銆傝В绛旇繃绋嬪涓嬶細棣栧厛瑕佷簡瑙inX鐨勫鏁版槸CosX銆傚啀鏍规嵁澶嶅悎鍑芥暟姹傚鍏紡Y'x=Y'u*Ux'銆傛妸2x鐪嬪仛涓涓暣浣搖銆傛眰sin2x鐨勫鏁帮紝灏辨槸鍏堟眰鍑簊inu鐨勫鏁般傜劧鍚庡啀鍦ㄥ2x姹傚銆傛渶鍚庣粨鏋滐細锛坰in2x锛'銆=(2x)'*(sinu)'銆=2cos2x銆傜瀛﹀簲鐢細瀵兼暟涓庣墿鐞嗗嚑浣曚唬鏁板叧绯诲瘑鍒.鍦ㄥ嚑浣曚腑鍙眰...
绛旓細sin2x鐨勫鏁帮細2cos2x銆傝В绛旇繃绋嬪涓嬶細棣栧厛瑕佷簡瑙inX鐨勫鏁版槸CosX銆傚啀鏍规嵁澶嶅悎鍑芥暟姹傚鍏紡Y'x=Y'u*Ux'銆傛妸2x鐪嬪仛涓涓暣浣搖銆傛眰sin2x鐨勫鏁帮紝灏辨槸鍏堟眰鍑簊inu鐨勫鏁般傜劧鍚庡啀鍦ㄥ2x姹傚銆傛渶鍚庣粨鏋滐細锛坰in2x锛'=(2x)'*(sinu)'=2cos2x
绛旓細sin2x鐨勫鏁版槸cos(2x) * 2銆俿in2x鐨勫鏁板彲浠ラ氳繃姹傚鍏紡杩涜璁＄畻銆傛牴鎹笁瑙掑嚱鏁扮殑姹傚瑙勫垯锛屽浜庡嚱鏁癴(x) = sin(ax)锛屽叾瀵兼暟涓篺'(x) = acos(ax)銆傚洜姝わ紝鎴戜滑鍙互灏唖in2x琛ㄧず涓篺(x) = sin(2x)锛屽苟搴旂敤涓婅堪姹傚鍏紡銆傚浜巗in2x锛屾垜浠彲浠ュ皢鍏剁湅浣滀竴涓鍚堝嚱鏁癴(u) = sin(u) * ...
绛旓細sin2x绛変簬2sinxcosx銆傝繖鍏跺疄鏄敱涓よ鍜岀殑姝ｅ鸡鍏紡sin(x+y)=sinxcosy+cosxsiny寰楀埌銆傛澶栵紝杩樻湁鍑犱釜涓夎鎭掔瓑寮廲os(x+y)=cosxcosy-sinxsinycos(x-y)=cosxcosy+sinxsinysin(x-y)=sinxcosy-cosxsinytan(x+y)=(tanx+tany)/(1-tanxtany)tan(x-y)=(tanx-tany)/(1+tanxtany)鎯虫帹瀵煎嚭鍚勭浜屽...
绛旓細sin2x鐨勫鏁帮細2cos2x銆俧(g(x))鐨勫鏁=f'(g(x))g'(x)鏈涓璮(x)鐪嬫垚 sinx g(x)鐪嬫垚2x鍗冲彲 (sin2x)'=2cos2x 鍦ㄥ叿浣撲竴鐐癸紝杩欎釜鍑芥暟姹傚鍏堢湅鏈澶栧眰鐨勫熀鏈嚱鏁皊in 鎯宠薄鎴恠iny siny鐨勫鏁版槸cosy 鎵浠ユ渶澶栧眰鍑芥暟鐨勫鏁颁负cosy 鍐嶇湅鍐呭眰鍑芥暟y=2x 杩炵画涓嶅彲瀵肩殑鏇茬嚎锛氬洜涓烘瘡涓鐐圭殑瀵兼暟閮戒笉瀛樺湪...
绛旓細瀵兼暟鏄-2sin2x銆俢os2x鐨勫鏁锛氾紞2sin2x銆傝繖鏄竴涓鍚堝嚱鏁扮殑瀵兼暟锛屾湁涓ゅ眰锛屽灞傛槸cos鐨勫鏁帮紝鍐呭眰鏄2x鐨勫鏁帮紝鎵浠ワ紙cos2x)'=-sin2x*(2x)鐨勫鏁帮紳-2sin2x銆傚鏁帮紝涔熷彨瀵煎嚱鏁板笺傚張鍚嶅井鍟嗭紝鏄井绉垎涓殑閲嶈鍩虹姒傚康銆俢os鐨勫惈涔 浣欏鸡锛堜綑寮﹀嚱鏁帮級锛屼笁瑙掑嚱鏁扮殑涓绉嶃傚湪Rt鈻矨BC锛堢洿瑙掍笁瑙掑舰锛変腑...
绛旓細y=sin2x鐨勫鏁版槸2cos2x銆傛嫇灞曠煡璇嗭細1銆佸鏁帮紙Derivative锛夛紝涔熷彨瀵煎嚱鏁板笺傚張鍚嶅井鍟嗭紝鏄井绉垎涓殑閲嶈鍩虹姒傚康銆傚綋鍑芥暟y=f锛坸锛夌殑鑷彉閲弜鍦ㄤ竴鐐箈0涓婁骇鐢熶竴涓閲徫攛鏃讹紝鍑芥暟杈撳嚭鍊肩殑澧為噺螖y涓庤嚜鍙橀噺澧為噺螖x鐨勬瘮鍊煎湪螖x瓒嬩簬0鏃剁殑鏋侀檺a濡傛灉瀛樺湪锛宎鍗充负鍦▁0澶勭殑瀵兼暟锛岃浣渇鈥欙紙x0锛夋垨df锛坸0...
绛旓細杩愮畻鏂规硶鏈変互涓嬩袱绉嶏細1.(sin²x)'= 2sinx(sinx)'= 2sinxcosx = sin2x銆2.(sin²x)'= [(1-cos2x)/2]'= [1/2 - (cos2x)/2]'= 0 - ½(-sin2x)(2x)'= ½(sin2x)脳2 = sin2x銆
绛旓細sin骞虫柟x鐨勫鏁鍙互鍐欐垚锛氾紙sin²x锛'=2sinx锛坰inx锛'=2sinxcosx=sin2x銆俿inx骞虫柟锛歽=sinx^2锛寉'=cosx^2*2x=2xcosx^2 瀵兼暟鏄鍑芥暟鍥惧儚鍦ㄦ煇涓鐐瑰鐨勬枩鐜囷紝涔熷氨鏄旱鍧愭爣澧為噺锛埼攜锛夊拰妯潗鏍囧閲忥紙螖x锛夊湪螖x-->0鏃剁殑姣斿笺傚井鍒嗘槸鎸囧嚱鏁板浘鍍忓湪鏌愪竴鐐瑰鐨勫垏绾垮湪妯潗鏍囧彇寰楀閲徫攛浠ュ悗锛...
绛旓細sin2x=2sinxcosx銆傚垎鏋愯繃绋嬪涓嬶細sin(伪+尾)=sin伪cos尾+ sin尾cos伪 sin(伪-尾)=sin伪cos尾-sinB*cos伪 鏍规嵁sin(伪+尾)=sin伪cos尾+ sin尾cos伪鍙緱锛歴in2x=sin锛坸+x锛=sinxcosx+sinxcosx=2sinxcosx
