复合函数求导cos(3x)是什么意思? lncos²3x求导等于多少
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
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\u6269\u5c55\u8d44\u6599\uff1a
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\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
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\u53c2\u8003\u8d44\u6599\u6765\u6e90\uff1a
\u767e\u5ea6\u767e\u79d1-\u5bfc\u6570
\u89e3:\u6839\u636e\u590d\u5408\u51fd\u6570\u7684\u5bfc\u6570\u516c\u5f0f\u5f97
\uff08lncos²3x\uff09'=2cos3x*(-sin3x)*3/cos²3x=-6tan3x
绛旓細cos(3x)'=-sin(3x)*(3x)'=-3sin(3x)
绛旓細浠=cosu锛寀=3x锛屾牴鎹澶嶅悎鍑芥暟鐨姹傚瑙勫垯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 鎵浠cos3x鐨勫鏁涓-3sin3x銆傚浜庡彲瀵肩殑鍑芥暟f(x)锛寈↦f'(x)涔熸槸涓涓嚱鏁帮紝绉颁綔f(x)鐨勫鍑芥暟锛堢畝绉板鏁帮級銆傚鎵惧凡鐭ョ殑鍑芥暟鍦ㄦ煇鐐圭殑瀵兼暟鎴栧叾瀵煎嚱鏁扮殑...
绛旓細浠锛漜osu锛寀锛3x锛屾牴鎹澶嶅悎鍑芥暟鐨勬眰瀵艰鍒檇y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锛锛囷紳锛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屼竴涓嚱鏁颁笉涓瀹氬湪鎵鏈夌偣閮芥湁瀵兼暟銆傚鏋鍑芥暟鐨勫鏁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
绛旓細浠=cosu锛寀=3x锛屾牴鎹澶嶅悎鍑芥暟鐨姹傚瑙勫垯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屼竴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1銆澶嶅悎杩囩▼锛寉=cosu锛寀=3x 2銆乴im(x->0)(1-cosx)/x² 锛0/0鍨嬩笂涓姹傚锛=lim(x->0)sinx/2x 锛坰inx/x=1锛=1/2
绛旓細閭ｅ氨鍏堢粰浣犱釜瀹氱悊澶嶅悎鍑芥暟f(g(x))鐨勫鏁涓篺'(g(x))*g'(x)鏈夎繖涓畾鐞嗗氨鍙互寰楀埌锛氬湪绗竴涓嚱鏁颁腑f(x)=x^2 g(x)=sinx鎵浠ュ鏁颁负2sinx*cosx=2sinxcosx鍚岀悊,鍦ㄧ浜屼釜鍑芥暟閲岄潰,f(x)=x^3 g(x)=cosx鎵浠ュ鏁颁负3cos^2x*-sinx...
绛旓細鎴戞墍璇寸殑瀹屽叏锛屽叾瀹炲氨鏄澶嶅悎鍑芥暟姹傚鐨勯摼寮忔硶鍒欒屽凡~~~瀵箈姹傚锛(sinx)'=cosx (sin3x)'=3*cos(3x)锛岃繖灏辨槸姹傚瑕佸畬鍏 浣嗘槸瀵3x姹傚锛(sin3x)'=cos3x 杩欒娉ㄦ剰鍖哄垎涓涓媬~~姹傚瑕佺湅瀵逛粈涔堟眰 杩欎釜鏍囧噯涓嶅悓锛屽鏁颁篃浼氶殢涔嬩笉鍚寏~~鍦ㄥ鏁颁腑锛屾崲鍏冩硶骞朵笉閫傜敤 鍥犱负瀵兼暟鏄竴涓彧涓庘柍x鏈夊叧鐨...
绛旓細2銆佸寲鎴恲=sin3x路3^(-x) 鐢(uv)'=u'v+uv'y'=cos3x路(3x)'路3^(-x)+sin3x路ln3路3^(-x)路(-x)'=3cos3x路3^(-x)-ln3路sin3x路3^(-x)=(3cos3x-ln3路sin3x)/3^x 缁撴灉鏄竴鏍风殑锛屾爣鍑嗙瓟妗堟病闂銆(sin3x銆3^(-x),閮芥槸澶嶅悎鍑芥暟锛屾眰瀵兼椂瑕佺敤鍒澶嶅悎鍑芥暟姹傚鍏紡锛
绛旓細3cos3x姹傚-9sin3x锛2cos2x姹傚-4sin2x
