求偏导数:（1）z=sin（xy）＋cos（x+y）（2）z=（1＋xy）的y次方 sin(x+z)=cos(y+z)一阶偏导数
\u6c42z=sin(xy)+cos^2(xy)\u7684y\u7684\u504f\u5bfcZy=ycos\uff08xy\uff09+2cos\uff08xy\uff09*[-sin\uff08xy\uff09]*x
=ycos\uff08xy\uff09-xsin\uff082xy\uff09
\u3000\u3000\u6c42\u5fae\u5206\uff0c\u6709
\u3000\u3000\u3000\u3000cos(x+z)*(dx+dz) = -sin(y+z)*(dy+dz)\uff0c
\u6574\u7406\u6210
\u3000\u3000\u3000\u3000dz = ----dx+----dy\uff0c
\u4e24\u4e2a\u504f\u5bfc\u6570\u5c31\u51fa\u6765\u4e86\u3002
绛旓細瀵逛簬鍑芥暟 y = sin(x)锛屽叾瀵兼暟涓猴細sin'(x) = cos(x)鐜板湪鎴戜滑瑕佹潵璁＄畻杩欎釜瀵兼暟鍜鍋忓鏁銆傝绠楃粨鏋滀负锛歴in(x) 鐨勫鏁颁负 cos(x)sin(x) 鐨勫亸瀵兼暟涓 0 鎵浠ワ紝sin(x) 鐨勫鏁颁负 cos(x)锛屽亸瀵兼暟涓 0銆
绛旓細姹傚亸瀵兼暟:(1)z=sin(xy)+cos(x+y)(2)z=(1+xy)鐨剏娆℃柟 鎴戞潵绛 1涓洖绛 #鐑# 璇ヤ笉璇ヨ瀛╁瓙寰堟棭瀛︿範浜烘儏涓栨晠?鐧惧害缃戝弸af34c30f5 2017-06-06 路 TA鑾峰緱瓒呰繃4.3涓囦釜璧 鐭ラ亾澶ф湁鍙负绛斾富 鍥炵瓟閲:1.8涓 閲囩撼鐜:65% 甯姪鐨勪汉:5087涓 鎴戜篃鍘荤瓟棰樿闂釜浜洪〉 鍏虫敞 灞曞紑鍏ㄩ儴 鏈洖...
绛旓細(1)斜z/斜x=cos(x^2*y^3)*2x 斜z/斜y=cos(x^2*y^3)*3y^2 (2)浠(x)=e^(xy),h(x)=y^2 鍒檇z=f'*g'+f'*h'=f'[(斜g/斜x)*dx+(斜g/斜y)*dy]+f'[(斜h/斜x)*dx+(斜h/斜y)*dy]=f'(ye^xydx+xe^xydy)+f'(2ydy)=f'ye^xydx+f'(xe^xy+2y)dy ...
绛旓細👉鍋忓鏁鐨勪緥瀛 銆庝緥瀛涓銆 z= x+y , ∂z/∂x =1 , ∂z/∂y=1 銆庝緥瀛愪簩銆 z= xy , ∂z/∂x =y , ∂z/∂y=x 銆庝緥瀛愪笁銆 z= xy^2 , ∂z/∂x =y^2 , ∂z/∂y=2xy 👉鍥...
绛旓細z=sin(xy)az/ax=cos(xy) *y=ycos(xy)az/ay=cos(xy) *x=xcos(xy)
绛旓細绗﹀悎闅愬嚱鏁板瓨鍦ㄥ畾鐞嗙殑鏉′欢锛岃兘纭畾闅愬嚱鏁皕=z(x,y)瀵筬姹傚亸瀵硷細fx=(yz)cos(xyz)fy=(xz)cos(xyz)fz=(xy)cos(xyz)-1 鍦ㄦ鍩虹涓婏紝鎴戜滑渚挎湁锛zx=-fx/fx=-(yz)cos(xyz) / [(xy)cos(xyz)-1]zy=-fy/fz=-(xz)cos(xyz) / [(xy)cos(xyz)-1]锛堟垨鑰咃紝鐩存帴瀵z=sin(xyz)涓よ竟鍚屾椂...
绛旓細1.鍏堟眰涓闃跺亸瀵,姣斿瀵箈姹備竴闃跺亸瀵,瀵箈姹傚亸瀵兼暟灏辨妸y鍜z瑙嗕负甯告暟,缁撴灉涓sin(xy)'(xy)'cos(yz)+sin(xy)cos(yz)'(yz)'=cos(xy)*y*cos(yz)-sin(xy)*sin(yz)*0=cos(xy)*y*cos(yz) //娉ㄦ剰(xy)' 瀵箈姹傚亸瀵兼椂缁撴灉涓簓,鍥犱负姝ゆ椂y涓哄父鏁.鐒跺悗鍐嶅y,z姹傚亸瀵,鍘熺悊鏄竴鏍风殑...
绛旓細閮暒鑽ｅ洖绛旓細浜屽厓鍑芥暟z=f锛坸锛寉锛夌殑浜岄樁鍋忓鏁鍏辨湁鍥涚鎯呭喌锛氾紙1锛∂z²/∂x²=[∂锛∂z/∂x锛塢/ ∂x锛涳紙2锛∂z²/∂y ²=[∂锛∂z/∂y锛塢/ ∂y锛涳紙3锛∂z²/锛&#...
绛旓細濡備笂鍥炬墍绀恒
绛旓細6.姹傚亸瀵兼暟锛歾=sin(x+xy) z'x=?: syms x y z=sin(x+x*y) diff(z,x) z'y : diff(z,y) z''xy=?:diff(diff(z,x),y)7.閲嶇Н鍒嗭細鈭玔0,1]dx鈭玔0,x]xydy: int(int(x*y,y,0,x),x,0,1)8.鏃犵┓绾ф暟锛氣垜[k=1,+鈭瀅1/[k(k+1)] syms k f...
