ln（2/x）求导 ln（2-x）的导数是多少。怎么求。
ln2x \u7684\u5bfc\u6570\u5e94\u8be5\u662f\u6c42ln\uff082\uff0dx\uff09\u7684\u5bfc\u6570\uff0c\u9996\u5148\u4ee4 2 - x\u4e3at\uff0c\u5219ln\uff082\uff0dx\uff09\u53ef\u5316\u4e3alnt
\u7136\u540e\uff0c\u6c42\u5bfc\u4e3a 1/t\u518d\u4e58\u4ee5t\u7684\u5bfc\u6570\uff0c
\u6700\u540e\u7b54\u6848\u4e3a -1/(2-x)\u3002
\u5982\u679c\u6ee1\u610f\u8bb0\u5f97\u91c7\u7eb3\u54e6\uff01
\u4f60\u7684\u597d\u8bc4\u662f\u6211\u524d\u8fdb\u7684\u52a8\u529b\u3002
(*^__^*) \u563b\u563b\u2026\u2026
\u6211\u5728\u6c99\u6f20\u4e2d\u559d\u7740\u53ef\u53e3\u53ef\u4e50\uff0c\u5531\u7740\u5361\u62c9ok\uff0c\u9a91\u7740\u72ee\u5b50\u8d76\u7740\u8682\u8681\uff0c\u624b\u4e2d\u62ff\u7740\u952e\u76d8\u4e3a\u4f60\u7b54\u9898\uff01\uff01\uff01
[ln（2/x）]'=(ln2-lnx)'=-1/x
绛旓細寰楀埌ln(2)=2锛岃В寰條n(2)=0.5锛屽洜姝わ紝ln2绛変簬0.5銆傛牴鎹鏁扮殑鍩烘湰鎬ц川浜岋紝褰搙涓鸿礋鏁版椂锛宭n(x)绛変簬ln(x+1)銆傚洜姝わ紝鍙互灏唜=-1浠ｅ叆璇ュ叕寮忥紝寰楀埌ln(-1)=-ln(2+1)锛岃В寰條n(-1)=-0.5銆傚洜姝わ紝ln2绛変簬-0.5銆
绛旓細ln(2)=0.69314718055995銆傝嚜鐒跺鏁版槸浠ュ父鏁癳涓哄簳鏁扮殑瀵规暟锛岃浣渓nN锛圢>0锛夈傚湪鐗╃悊瀛︼紝鐢熺墿瀛︾瓑鑷劧绉戝涓湁閲嶈鐨勬剰涔夛紝涓鑸〃绀烘柟娉曚负lnx銆傛暟瀛︿腑涔熷父瑙佷互logx琛ㄧず鑷劧瀵规暟銆
绛旓細瑙ｏ細鏍规嵁澶嶆暟鐨勫鏁拌绠楄鍒欙紝鏈塋nz=lnz+2k蟺i=ln涓▃涓+iargz+i2k蟺锛屽叾涓紝-蟺鈮rgz鈮は锛宬=卤1锛屄2锛屸︹︺傗埓Ln(2)=ln2+i2k蟺銆侺n(-1)=ln1+i蟺+i2k蟺=(2k+1)蟺i銆傗埖1+i=(鈭2)(1/鈭2+i/鈭2)=(鈭2)e^(蟺i/4)銆傗埓ln(1+i)=(1/2)ln2+蟺i/4銆備互澶嶆暟浣滀负鑷...
绛旓細ln 2绛変簬0.693147锛屾槸涓涓棤鐞嗘暟锛屼篃鏄竴涓秴瓒婃暟銆1銆乴n 2鐨勫惈涔 ln 2鏄嚜鐒跺鏁板嚱鏁扮殑鍊硷紝涔熷氨鏄互e涓哄簳鐨勫鏁板嚱鏁扮殑鍊笺俥鏄竴涓棤鐞嗘暟锛岀害绛変簬2.71828锛屾槸鑷劧鐣屼腑甯歌鐨勫父鏁颁箣涓銆俵n 2琛ㄧず婊¤冻e^x = 2鐨剎鐨勫硷紝涔熷氨鏄锛宔鐨勫灏戞鏂圭瓑浜2銆2銆乴n 2鐨勬ц川 ln 2鏄竴涓棤鐞嗘暟锛...
绛旓細ln2绾︾瓑浜0.69314718056銆傚叾涓紝ln琛ㄧず鑷劧瀵规暟锛屽畠鐨勫簳鏁版槸e锛堣嚜鐒跺父鏁帮級锛宔绾︾瓑浜2.71828銆傛墍浠ワ紝ln2瀹為檯涓婃槸e鐨勫灏戞鏂圭瓑浜2锛屽嵆e^x=2锛寈=ln2銆傛嫇灞曠煡璇嗭細1銆亂=lnx鐨勫畾涔夊煙涓簒鈭(0,+鈭)锛屽煎煙涓(-鈭,+鈭)锛屽浘褰㈠垎甯冨湪涓鍥涜薄闄愶紱涓哄崟璋冮掑锛岄潪濂囬潪鍋躲2銆乴nx鏄互e涓哄簳鐨勫鏁板嚱鏁帮紝...
绛旓細ln2锛屽嵆鑷劧瀵规暟鐨2娆℃柟锛屽叾鍊间唬琛ㄤ簡浠涓哄簳鏁版椂锛2鐨勫鏁般傚叿浣撹绠楁柟娉曞苟涓嶅鏉傦紝棣栧厛瑕佷簡瑙ｇ殑鏄嚜鐒跺鏁扮殑瀹氫箟锛屽嵆e鐨勬煇鏁版骞傜瓑浜2銆傛暟瀛︿笂锛屾垜浠湁 e^(ln2) = 2銆傝繖灏辨剰鍛崇潃锛宭n2鐨勫兼槸浣垮緱鑷劧瀵规暟绛変簬2鐨勯偅涓暟銆備簩銆佽绠楄繃绋嬭瑙 濡傛灉浣犳兂瑕佽绠條n2鐨勬暟鍊硷紝鍙互鍒╃敤瀵规暟鐨勬ц川銆備笅闈...
绛旓細鐢ㄥ埌鐨勭煡璇嗭細鎹㈠簳鍏紡 鍏蜂綋鎿嶄綔锛ln2-ln1 =log(e)2-log(e)1 =lg2/lg e-lg1/lg e (lg1=0)=lg2/lg e =ln2鈮0.6931471806
绛旓細ln2绾︾瓑浜0.693銆傝嚜鐒跺鏁版槸浠ュ父鏁癳涓哄簳鏁扮殑瀵规暟锛岃浣渓nN锛圢>0锛夈俥鏄竴涓棤闄愪笉寰幆灏忔暟锛屽叾鍊肩害绛変簬2.718銆傚洜姝わ紝ln2灏辨槸浠涓哄簳鏁帮紝2涓虹湡鏁扮殑瀵规暟銆傚鏁扮殑姒傚康鏈鍒濇槸鐢辩害缈·绾崇毊灏斿湪1614骞存彁鍑虹殑锛岀敤鏉ョ畝鍖栧鏉傛暟鍊艰绠椼傚鏁拌繍绠楁湁涓涓噸瑕佺殑鎬ц川锛岄偅灏辨槸瀹冨彲浠ユ妸涔橀櫎杩愮畻杞寲涓...
绛旓細3銆1闄や互ln2绛変簬浠涔堛4銆乴n2*ln2绛変簬浠涔堛1.ln2绛変簬0.6931銆2.ln鏄互e涓哄簳鐨勫鏁扮鍙凤紝鎵浠ヤ篃琚О涓鸿嚜鐒跺鏁般3.鑰宔鏄竴涓害绛変簬71828鈥︾殑鏃犵悊鏁般4.涓鑸儏鍐典笅锛屾垜浠細灏嗗叾鎹㈢畻鎴愪互鍗佷负搴曠殑甯哥敤瀵规暟锛屼粠lnx锛漧gx/lge杩欎釜鍏紡锛屽ln2杩涜鍙樺舰銆5.瀹冭浆鍖栦负ln2锛漧g2/lge銆
绛旓細1銆ln2閲岄潰鐨刲n鏄寚浠ヤ互10涓哄簳鐨勫鏁帮紝鍙堝洜涓簂n2涓嶅寘鎷垨鑰呰杩欎釜寮忓瓙閲岄潰娌℃湁鏈煡鏁癤锛屾墍浠ヨln2鏄竴涓父鏁 2銆亂=ln2锛屽氨鏄笉绠绛変簬鍑狅紝鍙嶆y=ln2銆傚洜姝=ln2鏄竴鏉″钩琛屼簬x杞寸殑鐩寸嚎銆傛墍浠'=0銆3銆佽嚜鐒跺鏁颁互甯告暟e涓哄簳鏁扮殑瀵规暟銆傝浣渓nN(N>0)銆傚湪鐗╃悊瀛︼紝鐢熺墿瀛︾瓑鑷劧绉戝涓湁閲嶈...
