法线和切线方程公式
法线斜率与切线斜率乘积为-1，用导数表示曲线y=f(x)在点M（x0,y0）处的切线方程为：y-f(x0)=f'(x0)(x-x0)。扩展资料
法线斜率与切线斜率乘积为-1，法线可以用一元一次方程来表示，与导数有直接的转换关系。用导数表示曲线y=f(x)在点M（x0,y0）处的切线方程为： y-f(x0)=f'(x0)(x-x0) 法线方程为: y-f(x0)=(-1/f'(x0))*(x-x0)。绛旓細1銆佹枩鐜囦笉涓鏍凤紱娉曠嚎鏂滅巼涓庡垏绾鏂滅巼涔樼Н涓-1锛屽嵆鑻ユ硶绾挎枩鐜鍜屽垏绾鏂滅巼鍒嗗埆鐢ㄎ便佄茶〃绀猴紝鍒欏繀鏈壩*尾=-1銆傛硶绾垮彲浠ョ敤涓鍏冧竴娆℃柟绋嬫潵琛ㄧず锛屽嵆娉曠嚎鏂圭▼銆備笌瀵兼暟鏈夌洿鎺ョ殑杞崲鍏崇郴銆2銆佹秹鍙婃柟闈笉涓鏍凤紱鍒囩嚎鏂圭▼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︾瓑鍐呭銆傛槸鍏充簬鍑犱綍鍥惧舰鐨...
绛旓細鏇茬嚎y=f(x)鍦ㄧ偣(x0,y0)锛堝叾涓瓂0=f(x0)锛夌殑鍒囩嚎鏂圭▼涓 y-y0=f'(x0)*(x-x0)鎴 y=y0+f'(x0)*(x-x0)=f(x0)+f'(x0)*(x-x0)鑰娉曠嚎鏂圭▼涓 f'(x0)*(y-y0)=-(x-x0)鎴 y=y0-锛1/f'(x0)锛*(x-x0)=f(x0)-锛1/f'(x0)锛*(x-x0)鍥犱负鍒囩嚎鍜屾硶绾鍨傜洿...
绛旓細6銆佺殑鍒囩嚎鏂圭▼涓 mxa^2+nyb^2=1 4杩囧弻鏇茬嚎 x^2a^2y^2b^2=1 涓婁竴鐐筆m锛宯鐨勫垏绾挎柟绋嬩负 mxa^2nyb^2=1 5杩囨姏鐗╃嚎 y^2=2px 涓婁竴鐐筆m锛宯鐨勫垏绾挎柟绋嬩负 ny=px+m銆7銆娉曠嚎鍜屽垏绾挎柟绋嬪叕寮鏄痽=f#39axa+fa鍜屛*尾=1娉曠嚎鏄寚濮嬬粓鍨傜洿浜庢煇骞抽潰鐨勮櫄绾垮湪鏁板鍑犱綍涓硶绾挎寚骞抽潰涓婂瀭鐩翠簬鏇茬嚎鍦ㄦ煇...
绛旓細鍒囩嚎鏂圭▼鍜屾硶绾挎柟绋嬬殑鍏崇郴鏄浉浜掑瀭鐩达紝鍏叡鐐规槸鍒囩偣锛岃繃鍒囩偣涓庡垏绾鍨傜洿鐨勭洿绾夸负娉曠嚎銆傝鏇茬嚎涓簓=f锛坸锛夊垯鍦ㄧ偣锛坅锛宖锛坅锛堬級澶勭殑鍒囩嚎鏂圭▼涓猴細y=f'锛坅锛夛紙x-a锛+f锛坅锛夛紝娉曠嚎鏂圭▼鍏紡锛毼*尾=-1銆傜敱鍩烘湰鍑芥暟鐨勫拰銆佸樊銆佺Н銆佸晢鎴栫浉浜掑鍚堟瀯鎴愮殑鍑芥暟鐨勫鍑芥暟鍒欏彲浠ラ氳繃鍑芥暟鐨勬眰瀵兼硶鍒欐潵鎺ㄥ銆傚垏...
绛旓細k = y ' = cos(鍏/3) = 1/2锛屽洜姝鍒囩嚎鏂圭▼涓 y - 鈭3/2 = 1/2*(x - 鍏/3) 锛娉曠嚎鏂圭▼涓 y - 鈭3/2 = -2*(x - 鍏/3) 銆
绛旓細璇存槑锛歗鈥斺旇〃绀烘鏂 y=1/x y'=-1/x^2 杩囩偣(1/2,2)鐨勫垏绾挎枩鐜囷細k=-1/(1/2)^2=-4 鍒囩嚎鏂圭▼锛歽-2=-4(x-1/2)y-2=-4x+2 4x+y-4=0 杩(1/2,2)鐨勬硶绾挎枩鐜囦负鍒囩嚎鏂滅巼鐨勮礋鍊掓暟锛1/4 娉曠嚎鏂圭▼锛歽-2=1/4(x-1/2)4y-8=x-1/2 8y-16=2x-1 2x-8y+15=0 ...
绛旓細1銆佽绠楁柟寮忎笉鍚 鍒囩嚎鏂圭▼鐨勮绠楁柟娉曟湁鍚戦噺娉曪紝鍒嗘瀽瑙ｆ瀽娉曪紝浠ｅ叆娉曠瓑銆傝娉曠嚎鏂圭▼鐨勮绠楁柟娉曪細娉曠嚎鏂滅巼涓庡垏绾鏂滅巼涔樼Н涓-1锛屽嵆鑻ユ硶绾挎枩鐜鍜屽垏绾鏂滅巼鍒嗗埆鐢ㄎ便佄茶〃绀猴紝鍒欏繀鏈壩*尾=-1銆傛硶绾垮彲浠ョ敤涓鍏冧竴娆℃柟绋嬫潵琛ㄧず锛屽嵆娉曠嚎鏂圭▼銆備笌瀵兼暟鏈夌洿鎺ョ殑杞崲鍏崇郴銆2銆佸畾涔変笉鍚 鍒囩嚎鏂圭▼瀹氫箟锛氭槸鐮旂┒鍒囩嚎浠ュ強...
绛旓細鍏充簬娉曠嚎鏂圭▼涓庡垏绾挎柟绋嬪叕寮锛屾硶绾挎柟绋嬭繖涓緢澶氫汉杩樹笉鐭ラ亾锛屼粖澶╂潵涓哄ぇ瀹惰В绛斾互涓婄殑闂锛岀幇鍦ㄨ鎴戜滑涓璧锋潵鐪嬬湅鍚э紒1銆佸浜庣洿绾裤2銆佹硶绾挎槸瀹冪殑鍨傜嚎锛屽浜庝竴鑸殑骞抽潰鏇茬嚎锛涙硶绾垮氨鏄垏绾跨殑鍨傜嚎锛涘浜庣┖闂村浘褰紝灏辫鍙樻垚娉曞钩闈簡銆3銆佹硶绾挎枩鐜囦笌鍒囩嚎鏂滅巼涔樼Н涓-1锛屽嵆鑻ユ硶绾挎枩鐜囧拰鍒囩嚎鏂滅巼鍒嗗埆鐢ㄎ便佄茶〃绀猴紝...
绛旓細y=1/e^t锛屽垯锛歟^t=1/y 鎵浠ワ紝x=2/y 鍗筹細y=2/x t=0锛屽垯锛歺=2锛寉=1 鎵浠ワ紝鍒囩偣涓(2,1)y'=-2/x²鍒囩嚎鏂滅巼k=y'(2)=-1/2锛屽垯娉曠嚎鏂滅巼涓2 鎵浠ワ紝鍒囩嚎鏂圭▼涓猴細x+2y-4=0锛娉曠嚎鏂圭▼涓猴細2x-y-3=0 绁濅綘寮蹇冿紒甯屾湜鑳藉府鍒颁綘锛屽鏋滀笉鎳傦紝璇疯拷闂紝绁濆涔犺繘姝ワ紒O(鈭鈭)...
绛旓細瑙ｏ細鈭靛嚱鏁颁负y=x^(1/3) 鈭存湁 y'=(1/3)x^(-2/3)鈭村嚱鏁板湪鐐(x锛寉)澶勭殑鍒囩嚎鏂滅巼涓 (1/3)x^(-2/3)鈭村嚱鏁板湪鐐(0锛0)澶勭殑鏂滅巼涓0锛鍒囩嚎鏂圭▼涓簓=0锛娉曠嚎鏂圭▼涓簒=0 瑙ｏ細鈭靛嚱鏁颁负y=ln(x+1) 鈭村嚱鏁扮殑瀵兼暟涓 y'=1/(x+1) 鈭村嚱鏁板湪鐐(-1锛0)澶 鐨勫垏绾挎枩鐜囦负...
