求数学y=arcsinx,y=arccosx,y=arctanx,函数图像 y=arcsinX、arccosX、arctanX、arcc...
\u505a\u51fay=arctanx\u7684\u51fd\u6570\u56fe\u50cfy=arctanx\u7684\u51fd\u6570\u56fe\u50cf\u5982\u4e0b\uff1a
\u51fd\u6570\u56fe\u50cf\u7684\u753b\u6cd5\uff1a\u7528\u5217\u8868\u7684\u65b9\u6cd5\u6765\u8868\u793a\u4e24\u4e2a\u53d8\u91cf\u4e4b\u95f4\u51fd\u6570\u5173\u7cfb\u7684\u65b9\u6cd5\u53eb\u505a\u5217\u8868\u6cd5\u3002\u8fd9\u79cd\u65b9\u6cd5\u7684\u4f18\u70b9\u662f\u901a\u8fc7\u8868\u683c\u4e2d\u5df2\u77e5\u81ea\u53d8\u91cf\u7684\u503c\uff0c\u53ef\u4ee5\u76f4\u63a5\u8bfb\u51fa\u4e0e\u4e4b\u5bf9\u5e94\u7684\u51fd\u6570\u503c\uff1b\u7f3a\u70b9\u662f\u53ea\u80fd\u5217\u51fa\u90e8\u5206\u5bf9\u5e94\u503c\uff0c\u96be\u4ee5\u53cd\u6620\u51fd\u6570\u7684\u5168\u8c8c\u3002
\u628a\u4e00\u4e2a\u51fd\u6570\u7684\u81ea\u53d8\u91cfx\u4e0e\u5bf9\u5e94\u7684\u56e0\u53d8\u91cfy\u7684\u503c\u5206\u522b\u4f5c\u4e3a\u70b9\u7684\u6a2a\u5750\u6807\u548c\u7eb5\u5750\u6807\uff0c\u5728\u76f4\u89d2\u5750\u6807\u7cfb\u5185\u63cf\u51fa\u5b83\u7684\u5bf9\u5e94\u70b9\uff0c\u6240\u6709\u8fd9\u4e9b\u70b9\u7ec4\u6210\u7684\u56fe\u5f62\u53eb\u505a\u8be5\u51fd\u6570\u7684\u56fe\u8c61\u3002
\u6269\u5c55\u8d44\u6599\uff1a
\u7531\u4e8e\u6b63\u5207\u51fd\u6570y=tanx\u5728\u5b9a\u4e49\u57dfR\u4e0a\u4e0d\u5177\u6709\u4e00\u4e00\u5bf9\u5e94\u7684\u5173\u7cfb\uff0c\u6240\u4ee5\u4e0d\u5b58\u5728\u53cd\u51fd\u6570\u3002\u6ce8\u610f\u8fd9\u91cc\u9009\u53d6\u662f\u6b63\u5207\u51fd\u6570\u7684\u4e00\u4e2a\u5355\u8c03\u533a\u95f4\u3002\u800c\u7531\u4e8e\u6b63\u5207\u51fd\u6570\u5728\u5f00\u533a\u95f4(-\u03c0/2,\u03c0/2)\u4e2d\u662f\u5355\u8c03\u8fde\u7eed\u7684\uff0c\u56e0\u6b64\uff0c\u53cd\u6b63\u5207\u51fd\u6570\u662f\u5b58\u5728\u4e14\u552f\u4e00\u786e\u5b9a\u7684\u3002
\u5f15\u8fdb\u591a\u503c\u51fd\u6570\u6982\u5ff5\u540e\uff0c\u5c31\u53ef\u4ee5\u5728\u6b63\u5207\u51fd\u6570\u7684\u6574\u4e2a\u5b9a\u4e49\u57df(x\u2208R\uff0c\u4e14x\u2260k\u03c0+\u03c0/2\uff0ck\u2208Z)\u4e0a\u6765\u8003\u8651\u5b83\u7684\u53cd\u51fd\u6570\uff0c\u8fd9\u65f6\u7684\u53cd\u6b63\u5207\u51fd\u6570\u662f\u591a\u503c\u7684\uff0c\u8bb0\u4e3a y=Arctan x\uff0c\u5b9a\u4e49\u57df\u662f(-\u221e\uff0c+\u221e)\uff0c\u503c\u57df\u662f y\u2208R\uff0cy\u2260k\u03c0+\u03c0/2\uff0ck\u2208Z\u3002
y=arcsinX Y'=1/(\u221a1-X²)
Y'= - 1/(\u221a1-X²)
Y'= 1/(1+X²)
Y'.= - 1/(1+X²)
\u7b54\u9898\u4e0d\u6613
\u795d\u4f60\u5b66\u4e60\u8fdb\u6b65
\u671b\u91c7\u7eb3 \u8c22\u8c22
绛旓細y=arcsinx鍙嶆寮﹀嚱鏁帮紝鍥惧儚璇︾粏瑙佷笅鍥撅細鍙嶆寮﹀嚱鏁帮紙鍙嶄笁瑙掑嚱鏁颁箣涓锛変负姝ｅ鸡鍑芥暟y=sinx锛坸鈭圼-½蟺,½蟺]锛夌殑鍙嶅嚱鏁帮紝璁颁綔y=arcsinx鎴杝iny=x锛坸鈭圼-1,1]锛夈傜敱鍘熷嚱鏁扮殑鍥惧儚鍜屽畠鐨勫弽鍑芥暟鐨勫浘鍍忓叧浜庝竴涓夎薄闄愯骞冲垎绾垮绉板彲鐭ユ寮﹀嚱鏁扮殑鍥惧儚鍜屽弽姝ｅ鸡鍑芥暟鐨勫浘鍍忎篃鍏充簬涓涓夎薄闄愯骞冲垎绾...
绛旓細arcsinx鐨勫鏁版槸锛歽'=1/cosy=1/鈭歔1-(siny)²]=1/鈭(1-x²)锛屾涓洪殣鍑芥暟姹傚銆傛帹瀵艰繃绋 y=arcsinx y'=1/鈭氾紙1-x²锛夊弽鍑芥暟鐨勫鏁帮細y=arcsinx,閭ｄ箞锛宻iny=x,姹傚寰楀埌锛宑osy*y'=1 鍗硑'=1/cosy=1/鈭歔1-(siny)²]=1/鈭(1-x²)闅愬嚱鏁板鏁扮殑姹傝В ...
绛旓細鎴戠殑 姹傛暟瀛=arcsinx,y=arccosx,y=arctanx,鍑芥暟鍥惧儚 1涓洖绛 #鐑# 浣滀负濂虫,浣犵敓娲讳腑鏈夋劅鍙楀埌鈥滀笉瀹夊叏鎰熲濈殑鏃跺埢鍚?鑷俊蹇冧笉楂 2014-09-24 路 瓒呰繃34鐢ㄦ埛閲囩撼杩嘥A鐨勫洖绛 鐭ラ亾绛斾富 鍥炵瓟閲:98 閲囩撼鐜:0% 甯姪鐨勪汉:67.6涓 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鏈洖绛旇鎻愰棶鑰呴噰绾 宸茶禐杩 ...
绛旓細y=arcsin鈭歺 瑙ｏ細y'=1/鈭歔1-(鈭歺)²]路(鈭歺)'=1/鈭(1-x)路1/(2鈭歺)=1/[2鈭(x-x²)]
绛旓細濡傛灉x=1,閭ｄ箞y绛変簬蟺/2
绛旓細浣跨敤鍙嶅嚱鏁板彲浠ュy=arcsinx姹傚锛氬洜涓y=arcsinx锛鎵浠ュ緱鍒 siny=x 绛夊紡涓よ竟瀵箈姹傚 y'cosy=1 鍙緱y'=1/cosy=1/鈭(1-sin^2(y))鍙緱y'= 1/鈭(1-x^2)涓夎鍑芥暟鐨勬眰瀵奸渶瑕佺敤鍒扮殑寮忓瓙锛(sinx)'=cosx銆(cosx)'=-sinx銆(tanx)'=sec²x=1+tan²x銆(cotx)'=-csc²x銆...
绛旓細y=arcsinx鐨勫畾涔夊煙鏄痆-1,1],鍊煎煙鏄痆-蟺/2,蟺/2]y=arccosx鐨勫畾涔夊煙鏄痆-1,1],鍊煎煙鏄痆0,蟺]y=arctanx鐨勫畾涔夊煙鏄(-鈭,+鈭),鍊煎煙鏄(-蟺/2,蟺/2)y=arccotx鐨勫畾涔夊煙鏄(-鈭,+鈭),鍊煎煙鏄(0,蟺)瀹氫箟鍩燂紙domain of definition锛夋寚鑷彉閲弜鐨勫彇鍊艰寖鍥达紝鏄嚱鏁颁笁瑕佺礌(瀹氫箟鍩熴佸煎煙銆佸搴...
绛旓細y=arcsinx鐨勫畾涔夊煙涓篬-1,1],鍊煎煙涓篬-蟺/2,蟺/2],鍙嶅嚱鏁版槸x=siny 鎵浠ヨ鍦╗-蟺/2,蟺/2]涓婃壘涓涓獃,浣縮iny=1,閭ｅ氨鏄痽=蟺/2鍜
绛旓細arcsinX 琛ㄧず涓涓搴︼紝鍏朵腑鐨刋鏄竴涓暟瀛楋紝-1<=X<=1銆俛rcsinX琛ㄧず鐨勮搴﹀氨鏄寚锛屾寮﹀间负X鐨勯偅涓銆arcsinx鏄寮﹀嚱鏁皊in鐨勫弽鍑芥暟 渚嬪:宸茬煡瑙掑害锛屽搴旂殑姝ｅ鸡鍊硷紝鍙啓鎴 sin30º=0.5 宸茬煡姝ｅ鸡鍊硷紝瀵瑰簲鐨勮搴︼紝鍙啓鎴 arc sin0.5=30º...
绛旓細arcsinx鐨勫鏁版槸锛歽'=1/cosy=1/鈭歔1-(siny)²]=1/鈭(1-x²)锛屾涓洪殣鍑芥暟姹傚銆傛帹瀵艰繃绋 y=arcsinx y'=1/鈭氾紙1-x²锛夊弽鍑芥暟鐨勫鏁帮細y=arcsinx,閭ｄ箞锛宻iny=x,姹傚寰楀埌锛宑osy*y'=1 鍗硑'=1/cosy=1/鈭歔1-(siny)²]=1/鈭(1-x²)闅愬嚱鏁板鏁扮殑姹傝В ...
