曲线y=lnx在点(1,0)处的切线方程是
\u66f2\u7ebfY=lnx\u5728\u70b9\uff081,0\uff09\u5904\u7684\u5207\u7ebf\u65b9\u7a0b\u4e3ay\u2032\uff1d1/x
k\uff1d1/1\uff1d1
y\uff1dx-1
绛旓細lnx鐨勫鏁版槸1/x锛屾墍浠y瀵锛1锛=1/x=1锛
绛旓細鏄 y = ln x 鍚э紵 涓嶇劧浣犲緱鎶婂簳鏁板憡璇夋垜 姹傚鏁皔'=(lnx)'=1/x褰搙=1鏃秠'=1鍗冲垏绾跨殑鏂滅巼鏄痥=y'=1璁剧洿绾挎槸y=x+b鍥犱负鐩寸嚎杩囩偣(1,0)鍒0=1+b鍒檅=-1鍒鏇茬嚎y=lnx鍦ㄧ偣锛1,0锛夊鐨勫垏绾挎柟绋嬫槸y=x-1
绛旓細= ln x+x*1/x= ln x+1 鎵浠=y'锛1锛=1 鍒囩嚎鏂圭▼涓猴細y-0=1*锛坸-1锛夋暣鐞嗕负锛歺-y-1=0 鑻鐐瑰湪鏇茬嚎涓婏紝鍏紡涓簓-f(a)=f'(a)(x-a)锛涜嫢鐐逛笉鍦ㄦ洸绾夸笂锛屽叕寮忎负y-f(x0)=f'(x0)(x-x0)銆傚垏绾挎柟绋嬫槸鐮旂┒鍒囩嚎浠ュ強鍒囩嚎鐨勬枩鐜囨柟绋嬶紝娑夊強鍑犱綍銆佷唬鏁般佺墿鐞嗗悜閲忋侀噺瀛愬姏瀛︾瓑鍐呭銆
绛旓細瀵y锛銖憍姹傚锛寉'锛1锛弜锛坸锛0锛.浠锛1,灏卞彲姹傚嚭鍏舵枩鐜囦负1銆傛晠鍒囩嚎鏂圭▼涓簓锛漻.涓庡潗鏍囪酱鍥存垚鐨勭洿瑙掕竟涓1鐨勭瓑鑵扮洿瑙掍笁瑙掑舰锛岄潰绉槸0.5
绛旓細lnx鏄互e涓哄簳鐨勫鏁板嚱鏁帮紝鍏朵腑e鏄竴涓棤闄愪笉寰幆灏忔暟锛屽叾鍊肩害绛変簬2.718281828459鈥﹀嚱鏁扮殑鍥捐薄鏄繃鐐癸紙1,0锛鐨勪竴鏉鍨嬬殑鏇茬嚎,涓茶繃绗竴锛岀鍥涜薄闄愶紝涓旂鍥涜薄闄愮殑鏇茬嚎閫愭笎闈犺繎Y 杞达紝浣嗕笉鐩镐氦锛岀涓璞¢檺鐨勬洸绾块愭笎鐨勮繙绂籜杞淬傚叾瀹氫箟鍩燂細x>0 鍊煎煙锛y锛堟棤绌凤級...
绛旓細璁惧垏绾挎柟绋嬩负锛y=k锛坸-1锛鐢变簬dydx=lnx+1鏁咃細k=1鎵浠ュ垏绾挎柟绋嬩负锛歽=x-1
绛旓細y=x鐨勫浘鍍忎笌y=lnx鐨勫浘鍍忔槸娌℃湁浜ょ偣鐨勶紝涓よ呭苟涓嶄細鐩镐氦銆傚嚱鏁帮細鍏朵腑y=x鐨勫嚱鏁板浘鍍忔槸涓鏉¤繃鍘熺偣鐨勭洿绾匡紝鍥惧儚缁忚繃涓銆佷笁璞¢檺锛屽苟涓旀槸涓銆佷笁璞¢檺鐨勮骞冲垎绾匡紝鍑芥暟鍥惧儚鍦ㄦ暣涓畾涔夊尯闂村崟璋冮掑銆傝寉=lnx鐨勫嚱鏁板浘鍍忔槸涓鏉¤繃鐐癸紙1,0锛鐨鏇茬嚎锛屽叾瀹氫箟鍩熶负锛0锛+鈭烇級锛屽湪x=1鏃讹紝y=lnx鐨勫嚱鏁板浘鍍忎笌y=...
绛旓細鍒囩偣锛氾紙1,ln1锛=(1,0)y'=1/x k=1 鎵浠ュ垏绾挎柟绋嬩负 y-0=1脳锛坸-1锛夊嵆y=x-1
绛旓細瑙g敱y=(x+1)lnxl 姹傚寰梱'=(x+1)'lnx+(x+1)(lnx)'=lnx+(x+1)/x 鏁呭綋x=1鏃,y'=ln1+(1+1)/2=2 鏁卥=2 鏁呭垏绾挎柟绋嬩负y-0=2(x-1)鍗充负2x-y-2=0
绛旓細y'=lnx +x/x=lnx +1 y'|x=1=ln1+1=1 鏁呭垏绾夸负y=x-1 娉曠嚎涓簓=-(x-1)=-x+1