函数y=x分之sinx的导数wei为什么是1 y=x/sinx的导数怎么求
y=sinx\u5728x=0\u5904\u5bfc\u6570\u4e3a\u4ec0\u4e48\u662f1
\u5bfc\u6570\u7684\u51e0\u4f55\u610f\u4e49\uff1a\u5bfc\u51fd\u6570\u7684\u503c\u662f\u8be5\u51fd\u6570\u66f2\u7ebf\u5728\u8fd9\u4e00\u70b9\u4e0a\u7684\u5207\u7ebf\u659c\u7387\u3002
y=sinx\u5728x=0\u5904\u7684\u5207\u7ebf\u662fy=x\uff0c\u659c\u7387=1\u2192y'(0)=1
(sinx)'=lim[sin(x+\u25b3x)-sinx]/\u25b3xsin(x+\u25b3x)-sinx=2cos(x+\u25b3x/2)sin(\u25b3x/2)\u6ce8\u610f\u25b3x\u21920\u65f6, [sin(\u25b3x/2)]/(\u25b3x/2)\u21921\u6240\u4ee5(sinx)'=lim[2cos(x+\u25b3x/2)sin(\u25b3x/2)]/\u25b3x=lim[cos(x+\u25b3x/2)][sin(\u25b3x/2)]/(\u25b3x/2)=cosx
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绛旓細瀵兼暟涓猴紙-1/x^2锛塩os(1/x)瀵逛簬鍙屾洸鍑芥暟sinh x锛宑osh x锛宼anh x绛変互鍙婂弽鍙屾洸鍑芥暟arsinh x锛宎rcosh x锛宎rtanh x绛夊拰鍏朵粬杈冨鏉傜殑澶嶅悎鍑芥暟姹傚鏃堕氳繃鏌ラ槄瀵兼暟琛ㄥ拰杩愮敤寮澶寸殑鍏紡涓 y=u卤v鐨勫鍑芥暟涓簓'=u'卤v'銆亂=uv鐨勫鍑芥暟涓簓=u'v+uv'鍧囪兘杈冨揩鎹峰湴姹傚緱缁撴灉銆
绛旓細鍏蜂綋鍥炵瓟濡備笅锛歽=sinx /x y'=锛坰inx /x锛'=銆愶紙sinx锛' *x -sinx *x'銆 /x^2 锛坰inx锛'=cosx锛寈'=1銆傛墍浠ワ細y'=锛坈osx *x -sinx锛 /x^2 瀵兼暟鐨勬剰涔夛細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...
绛旓細y'=(xcosx-sinx)/x^2
绛旓細鍘熷紡=鈭(cosx)^4 dx =鈭(1-sinx^2)cosx^2dx =鈭玞osx^2dx-鈭玸inx^2cosx^2dx =鈭(1/2)(1+cos2x)x-鈭(1/4)[(1-cos4x)/2]dx =(x/2)+(1/4)sin2x-(x/8)+(1/32)sin4x+C =3x/8+(1/4)sin2x+(1/32)sin4x+C
绛旓細y'=(xcosx-sinx)/x^2
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