根号下怎么求导
根号就是表示某数开2分之1次根。
公式是 (x^n)'=nx^(n-1)
绛旓細鏍瑰彿灏辨槸琛ㄧず鏌愭暟寮2鍒嗕箣1娆℃牴銆鍏紡鏄 (x^n)'=nx^(n-1)鍏紡鐨勬剰鎬濇槸x鐨刵娆℃柟姹傚锛岀瓑浜巒涔樹互x鐨刵-1娆℃柟銆備緥濡傦細鈭歺 = x鐨2鍒嗕箣1娆℃柟 =锛坸锛塣锛1/2锛夋眰瀵 锛1/2锛 x ^锛1/2 - 1 锛= 锛1/2锛 x ^锛 - 1/2 锛= 1 / 锛2鈭歺锛夊張濡傦細y = a寮3娆℃柟姹傚锛屻恲 =...
绛旓細锛1锛夐鍏堝皢鏍瑰彿涓殑琛ㄨ揪寮忓寲绠锛岀敤涓涓父鏁癱鏇挎崲鏍瑰彿涓殑琛ㄨ揪寮忥紝鍗硑=鈭(c+x)锛涳紙2锛鍒╃敤鏋侀檺娉曟眰瀵锛氱敱瀹氫箟鍙煡锛寉'=f'(x)=lim螖y/螖x鈫0,鍗硑'=lim(鈭(c+x+螖x)-鈭(c+x))/螖x鈫0 灏嗏垰(c+x+螖x)-鈭(c+x)鍒嗗紑鍒嗘瘝鍒嗗瓙璁＄畻锛氬垎瀛愶細鈭(c+x+螖x)-鈭(c+x)=(c+x+螖x...
绛旓細1銆佸鏍瑰彿澶栫殑鍑芥暟姹傚銆2銆佸鏍瑰彿鍐呯殑鍑芥暟姹傚骞朵箻浠ユ牴鍙峰鐨勫嚱鏁板鏁般3銆佷箻浠ユ牴鍙峰唴鍑芥暟瀵兼暟鐨勫掓暟銆傝鍑芥暟涓簓=鈭歠锛坸锛夛紝鏍规嵁閾惧紡娉曞垯锛屽f锛坸锛夋眰瀵煎緱鍒癴鈥橈紙x锛夛紝璁＄畻鈭歠锛坸锛夌殑瀵兼暟锛屽嵆锛堚垰f锛坸锛夛級鈥=1/锛2鈭歠锛坸锛夛級锛屾牴鎹箻娉曟硶鍒欙紝灏嗕袱鑰呯浉涔樺緱鍒皔鈥=锛1/锛2鈭歠锛坸锛夛級锛*...
绛旓細(1/2)*x^(-1/2)銆備緥濡傦紝瀵箉=鈭歺姹傚锛搴旂敤涓婅堪鍏紡寰楀埌锛歽' = (1/2)*x^(-1/2) = 1/鈭歺銆傚悓鏍峰湴锛屽鏋滄眰y=x^(1/3)鐨勫鏁帮紝搴旂敤鍏紡锛歽' = (1/3)*x^(-2/3) = 1/(3鈭歺^2)銆傝繖涓鍒欓傜敤浜庢墍鏈夊舰濡倅=x^(1/n)鐨勫嚱鏁帮紝鍏朵腑n涓烘鏁存暟銆傚鏁扮殑缁撴灉鏄細y' = (1/n...
绛旓細1銆佸灞傚嚱鏁板氨鏄竴涓牴鍙凤紝鎸夋牴鍙锋眰涓涓鏁般2銆佺劧鍚庡湪姹傚唴灞傚嚱鏁颁篃灏辨槸鏍瑰彿閲岄潰鐨勫嚱鏁扮殑瀵兼暟銆3銆佷袱鑰呯浉涔樺氨琛屼簡銆備妇渚嬭鏄庯細鈭氾紙x+3锛夋眰瀵=1/2脳1/鈭氾紙x+3锛壝楋紙x+3锛=1/2鈭氾紙x+3锛夈傚叾瀹炴牴鍙峰氨鏄1/2娆℃柟锛屼綘浼氭眰x骞虫柟瀵兼暟灏变細甯︽牴鍙风殑姹傚浜嗐
绛旓細鏍瑰彿姹傚鍏紡锛氣垰x=x鐨2鍒嗕箣1娆℃柟銆傛牴鍙锋槸涓涓暟瀛︾鍙枫傛牴鍙锋槸鐢ㄦ潵琛ㄧず瀵逛竴涓暟鎴栦竴涓唬鏁板紡杩涜寮鏂硅繍绠楃殑绗﹀彿銆傝嫢a^n=b锛岄偅涔坅鏄痓寮n娆℃柟鐨刵娆℃柟鏍规垨a鏄痓鐨1/n娆℃柟銆傚紑n娆℃柟鎵嬪啓浣撳拰鍗板埛浣撶敤鏍瑰彿琛ㄧず锛岃寮鏂圭殑鏁版垨浠ｆ暟寮忓啓鍦ㄧ鍙峰乏鏂箆褰㈤儴鍒嗙殑鍙宠竟鍜岀鍙蜂笂鏂逛竴妯儴鍒嗙殑涓嬫柟鍏卞悓鍖呭洿鐨勫尯鍩...
绛旓細鏍瑰彿姹傚鏂规硶濡備笅锛1銆佸灞傚嚱鏁板氨鏄竴涓牴鍙凤紝鎸夋牴鍙锋眰涓涓鏁般2銆佺劧鍚庡湪姹傚唴灞傚嚱鏁扮殑瀵兼暟锛屼篃灏辨槸鏍瑰彿閲岄潰鐨勫嚱鏁扮殑瀵兼暟銆倅=鈭歺=x^1/2锛泍鈥=1/2*x^锛1/2-1锛=x^锛-1/2锛/2=1/锛2鈭歺锛夈傝嫢y=f锛坸锛夎〃绀烘煇鍑芥暟锛屽垯鍏跺鏁皔鈥=f鈥欙紙x锛夊畾涔変负锛氬綋x鐨勫彉鍖栭噺螖x瓒嬩簬闆舵椂锛屽嚱鏁癴...
绛旓細閫氬父锛鏍瑰彿灏辨槸琛ㄧず鏌愭暟寮2鍒嗕箣1娆℃牴銆備緥濡傦細鈭歺 = x鐨2鍒嗕箣1娆℃柟 =锛坸锛塣锛1/2锛姹傚 锛1/2锛 x ^锛1/2 - 1 锛= 锛1/2锛 x ^锛 - 1/2 锛= 1 / 锛2鈭歺锛夊張濡傦細y = a寮3娆℃柟姹傚锛屻恲 = a^(1/3) 銆憏' = 锛1/3锛塧^ 锛1/3 - 1 锛夊欢浼歌嚦寮涓涓暟鐨刵娆℃柟...
绛旓細姹鏍瑰彿涓鐨勫鏁版楠ゅ涓嬶細1銆佸皢鏍瑰彿澶栫殑鍑芥暟鎸夌収x杩涜寰垎锛屽緱鍒颁竴涓惈鏈夋牴鍙风殑寮忓瓙銆2銆佸皢鏍瑰彿鍐呯殑寮忓瓙杩涜鎭掔瓑鍙樺舰锛屼娇寰楀叾鎸囨暟涓2銆3銆佸鍙樺舰鎴愬瀷鐨勫紡瀛愯繘琛姹傚锛屽緱鍒版渶缁堢殑瀵兼暟銆傛牴鍙穢锛堚垰x锛夋槸涓涓父瑙佺殑鏁板鍑芥暟锛岃〃绀簒鐨勫钩鏂规牴銆傚鏁版槸鎻忚堪鍑芥暟鍦ㄦ瘡涓偣澶勭殑鏂滅巼锛堝彉鍖栫巼锛夌殑姒傚康銆傛牴鍙穢鐨勫鏁...
绛旓細鏍瑰彿姹傚鍏紡锛氣垰x=x鐨2鍒嗕箣1娆℃柟銆傛牴鍙锋槸涓涓暟瀛︾鍙枫傛牴鍙锋槸鐢ㄦ潵琛ㄧず瀵逛竴涓暟鎴栦竴涓唬鏁板紡杩涜寮鏂硅繍绠楃殑绗﹀彿銆傝嫢a^n=b锛岄偅涔坅鏄痓寮n娆℃柟鐨刵娆℃柟鏍规垨a鏄痓鐨1/n娆℃柟銆傚紑n娆℃柟鎵嬪啓浣撳拰鍗板埛浣撶敤鏍瑰彿琛ㄧず锛岃寮鏂圭殑鏁版垨浠ｆ暟寮忓啓鍦ㄧ鍙峰乏鏂箆褰㈤儴鍒嗙殑鍙宠竟鍜岀鍙蜂笂鏂逛竴妯儴鍒嗙殑涓嬫柟鍏卞悓鍖呭洿鐨勫尯鍩...
