cos^3x求导,则,f撇零等于多少 3cos3x求导是多少？图片里是怎么求导的？
Cos3x\u6c42\u5bfc\u4ee4y\uff1dcosu\uff0cu\uff1d3x\uff0c\u6839\u636e\u590d\u5408\u51fd\u6570\u7684\u6c42\u5bfc\u89c4\u5219dy\uff0fdx\uff1d\uff08dy\uff0fdu\uff09\uff0a\uff08du\uff0fdx\uff09
y\uff07\uff1d\uff08cosu\uff09\uff07\uff083x\uff09\uff07\uff1d\uff0d3sinu\uff0cu\u66ff\u6362\u4e3a3x\uff0c\u6700\u7ec8\u7ed3\u679cy\uff07\uff1d\uff0d3sin3x
\u4e0d\u662f\u6240\u6709\u7684\u51fd\u6570\u90fd\u6709\u5bfc\u6570\uff0c\u4e00\u4e2a\u51fd\u6570\u4e0d\u4e00\u5b9a\u5728\u6240\u6709\u70b9\u90fd\u6709\u5bfc\u6570\u3002\u5982\u679c\u51fd\u6570\u7684\u5bfc\u6570\u5b58\u5728\u4e8e\u67d0\u4e00\u70b9\uff0c\u5219\u5728\u8fd9\u4e00\u70b9\u4e0a\u79f0\u4e3a\u53ef\u5fae\u7684\uff0c\u5426\u5219\u79f0\u4e3a\u4e0d\u53ef\u5fae\u7684\u3002\u7136\u800c\uff0c\u53ef\u5fae\u51fd\u6570\u5fc5\u987b\u662f\u8fde\u7eed\u7684\uff1b\u4e0d\u8fde\u7eed\u51fd\u6570\u4e0d\u80fd\u662f\u53ef\u5fae\u7684\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u51fd\u6570y\uff1df\uff08x\uff09\u7684\u5bfc\u6570f\u2019\uff08x0\uff09\u5728x0\u70b9\u7684\u51e0\u4f55\u610f\u4e49\uff1a\u51fd\u6570\u66f2\u7ebf\u5728P0\u70b9\u7684\u5207\u7ebf\u659c\u7387\uff08x0\uff0cf\uff08x0\uff09\uff09\uff08\u5bfc\u6570\u7684\u51e0\u4f55\u610f\u4e49\u662f\u51fd\u6570\u66f2\u7ebf\u5728\u8be5\u70b9\u7684\u5207\u7ebf\u659c\u7387\uff09\u3002
\u5982\u679c\u4e00\u4e2a\u51fd\u6570\u7684\u5bfc\u51fd\u6570\u5728\u67d0\u4e00\u533a\u95f4\u5185\u603b\u662f\u5927\u4e8e\u96f6\uff08\u6216\u5c0f\u4e8e\u96f6\uff09\uff0c\u5219\u8be5\u51fd\u6570\u5728\u8be5\u533a\u95f4\u5185\u662f\u5355\u8c03\u9012\u589e\uff08\u6216\u9012\u51cf\uff09\u7684\uff0c\u4e5f\u5c31\u662f\u8be5\u51fd\u6570\u7684\u5355\u8c03\u533a\u95f4\u3002\u5bfc\u6570\u51fd\u6570\u7b49\u4e8e\u96f6\u7684\u70b9\u79f0\u4e3a\u51fd\u6570\u7684\u5e73\u7a33\u70b9\u3002\u5728\u8fd9\u4e00\u70b9\u4e0a\uff0c\u51fd\u6570\u53ef\u4ee5\u5f97\u5230\u6700\u5927\u503c\u6216\u6700\u5c0f\u503c\uff08\u5373\u6781\u503c\u7684\u53ef\u7591\u70b9\uff09\u3002
\u5bf9\u4e8e\u4e00\u4e2a\u6ee1\u610f\u7684\u70b9\uff0c\u5982\u679c\u5b83\u5b58\u5728\uff0c\u4f7f\u5f97\u5b83\u5728\u524d\u4e00\u4e2a\u533a\u95f4\u5927\u4e8e\u6216\u7b49\u4e8e\u96f6\uff0c\u5728\u540e\u9762\u7684\u533a\u95f4\u4e2d\u5c0f\u4e8e\u6216\u7b49\u4e8e\u96f6\uff0c\u5219\u5b83\u662f\u4e00\u4e2a\u6700\u5927\u70b9\uff0c\u5426\u5219\u5b83\u662f\u4e00\u4e2a\u6700\u5c0f\u70b9\u3002
\u5f53x\u6539\u53d8\u65f6\u51fd\u6570\u7684\u5207\u7ebf\u53d8\u5316\uff08\u84dd\u8272\u66f2\u7ebf\uff09\u3002\u51fd\u6570\u7684\u5bfc\u6570\u503c\u662f\u5207\u7ebf\u7684\u659c\u7387\u3002\u7eff\u8272\u8868\u793a\u5176\u503c\u4e3a\u6b63\uff0c\u7ea2\u8272\u8868\u793a\u5176\u503c\u4e3a\u8d1f\uff0c\u9ed1\u8272\u8868\u793a\u5176\u503c\u4e3a\u96f6\u3002
\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a
\u767e\u5ea6\u767e\u79d1-\u5bfc\u6570
3cos3x\u6c42\u5bfc-9sin3x\uff0c2cos2x\u6c42\u5bfc-4sin2x
绛旓細f'(x)=-3sinx(cosx)^2. f'(0)=0. 鍥犱负sin0=0锛屽畠鍜屼换浣曟暟鐨勭Н绛変簬0.浣犵殑寮忓瓙瑕佹墦濂戒竴鐐癸紝搴旇鏄(cosx)^3.
绛旓細浠锛漜osu锛寀锛3x锛屾牴鎹鍚堝嚱鏁扮殑姹傚瑙勫垯dy锛廳x锛濓紙dy锛廳u锛夛紛锛坉u锛廳x锛墆锛囷紳锛坈osu锛夛紘锛3x锛夛紘锛濓紞3sinu锛寀鏇挎崲涓3x锛屾渶缁堢粨鏋測锛囷紳锛3sin3x 涓嶆槸鎵鏈夌殑鍑芥暟閮芥湁瀵兼暟锛涓涓嚱鏁颁笉涓瀹氬湪鎵鏈夌偣閮芥湁瀵兼暟銆傚鏋滃嚱鏁扮殑瀵兼暟瀛樺湪浜庢煇涓鐐癸紝鍒欏湪杩欎竴鐐逛笂绉颁负鍙井鐨勶紝鍚﹀垯绉颁负涓嶅彲寰殑銆傜劧鑰...
绛旓細浠=cosu锛寀=3x锛屾牴鎹鍚堝嚱鏁扮殑姹傚瑙勫垯dy/dx=(dy/du)*(du/dx)y'=(cosu)'(3x)'=-3sinu锛寀鏇挎崲涓3x锛屾渶缁堢粨鏋測'=-3sin3x 涓嶆槸鎵鏈夌殑鍑芥暟閮芥湁瀵兼暟锛涓涓嚱鏁颁篃涓嶄竴瀹氬湪鎵鏈夌殑鐐逛笂閮芥湁瀵兼暟銆傝嫢鏌愬嚱鏁板湪鏌愪竴鐐瑰鏁板瓨鍦紝鍒欑О鍏跺湪杩欎竴鐐瑰彲瀵硷紝鍚﹀垯绉颁负涓嶅彲瀵笺傜劧鑰岋紝鍙鐨勫嚱鏁颁竴瀹氳繛缁紱...
绛旓細姝ｅ鸡鍊掓暟涓烘锛屼綑寮﹀掓暟涓鸿礋銆傜幇瀵瑰唴灞姹傚锛屽湪瀵瑰灞傛眰瀵笺傚唴灞備负3X锛屾眰瀵煎緱3銆傚灞備负COS3X锛屾眰瀵煎緱锛峉IN3X銆傜劧鍚庣浉涔樸侽K浜嗭紒
绛旓細瑙ｇ瓟杩囩▼濡備笅锛氫竴鑸畾鐞嗭細1銆佸畾鐞1锛氳f(x)鍦ㄥ尯闂碵a,b]涓婅繛缁锛屽垯f(x)鍦╗a,b]涓婂彲绉2銆佸畾鐞2锛氳f(x)鍖洪棿[a,b]涓婃湁鐣岋紝涓斿彧鏈夋湁闄愪釜闂存柇鐐癸紝鍒檉(x)鍦╗a,b]涓婂彲绉3銆佸畾鐞3锛氳f(x)鍦ㄥ尯闂碵a,b]涓婂崟璋冿紝鍒檉(x)鍦╗a,b]涓婂彲绉
绛旓細f(x)=cos3x銆鍒檉(x+2蟺)=cos[3(x+2蟺)]=cos(3x+6蟺)=cos(3x+3*2蟺)銆備护a=3x銆傚垯f(x+2蟺)=cos(a+3*2蟺)銆傚洜涓篶os鐨勫懆鏈熸槸2蟺銆傛墍浠os(a+3*2蟺)=cosa銆
绛旓細灏辨湰棰樿岃█鍙瘉鏄庡涓嬶細璁f(t)鐨勫師鍑芥暟涓F(t)锛屽畾绉垎鐨勭粨鏋滃氨鏄疐(cos3x)-F(0)锛岀敤瀹冨啀瀵x 姹傚灏辫兘寰楀埌鎵姹傜粨鏋溿傛敞鎰廎(0)涓哄父閲忓叾瀵兼暟涓闆銆傝繕鏈夎瑙ｅ喅杩欎釜闂浣犲繀椤昏浼氬鍚堝嚱鏁扮殑姹傚銆
绛旓細cosx鐨勫鏁鏄-sinx銆傚嵆y=cosx y'=-sinx銆傝瘉鏄庤繃绋嬶細1銆佺敤鍜屽樊鍖栫Н鍏紡cos(a) - cos(b) = - 2sin[(a+b)/2]sin[(a-b)/2]銆2銆侀噸瑕佹瀬闄恖im(h->0) sin(h)/h = 1銆
绛旓細瀵兼暟鏋侀檺瀹氱悊鏄锛氬鏋渇(x)鍦▁0鐨勬煇棰嗗煙鍐呰繛缁紝鍦▁0鐨勫幓蹇冮偦鍩熷唴鍙锛屼笖瀵煎嚱鏁板湪x0澶勭殑鏋侀檺瀛樺湪锛堢瓑浜巃锛锛屽垯f(x)鍦▁0澶鐨勫鏁涔熷瓨鍦ㄥ苟涓旂瓑浜巃銆傝繖涓畾鐞嗙殑閲嶈涔嬪鍦ㄤ簬锛屼笉浜嬪厛瑕佹眰f鍦▁0澶勫彲瀵硷紝鑰屾牴鎹鍑芥暟鐨勬瀬闄愬瓨鍦ㄥ氨鑳芥帹鍑哄湪璇ョ偣鍙锛屼篃灏辨槸璇达紝瀵煎嚱鏁板鏋滃湪鏌愮偣鏋侀檺瀛樺湪锛岄偅涔堝湪...
绛旓細瑙ｏ細鈭(0,蟺/2)(sinx)^9dx =鈭(0,蟺/2)(sinx)^8*sinxdx =鈭(0,蟺/2)((sinx)^2)^4*sinxdx =-鈭(0,蟺/2)(1-(cosx)^2)^4dcosx 浠osx=t锛岄偅涔堬紝-鈭(0,蟺/2)(1-(cosx)^2)^4dcosx =-鈭(1,0)(1-t^2)^4dt =鈭(0,1)(1-t^2)^4dt =鈭(0,1)(t^8-4t^6...
