x+yln+xy+隐函数求导

危彼薛2919问一道高数题已知隐函数xy=x+lny,求y' y+xy'=1+y'/y 这一步是怎么来的啊, -
弓沫群13988312935 ______[答案] 左右两边同时对x求导,y是x的函数,故等式左边为:(xy)'=x'y+y'x=y+y'x. 右边为:(x+lny)'=x'+(lny)'=1+(1/y)y'=1+y'/y.

危彼薛2919求下列隐函数的微分dy:求下列隐函数的微分dy:1.y=tan(x+y) 2.y^2=x+lny -
弓沫群13988312935 ______[答案] 1. dy=[sec(x+y)]^2*d(x+y) [cos(x+y)]^2*dy=dx+dy -[sin(x+y)]^2*dy=dx dy=-[csc(x+y)]^2*dx 2. d(y^2)=d(x+lny) 2ydy=dx+dy/y (2y-1/y)dy=dx dy=ydx/(2y^2-1)

危彼薛2919关于求隐函数的导数dy/dx问题我没有输完就提问了方程xy=e^(x+y)我是这样做的lnxy = x+y;lnx + lny = x+y两边取导数1/x+1/y*(dy/dx) = 1+dy/dxdy/dx = ((1 - x)y)/((1 - y)... -
弓沫群13988312935 ______[答案] 对于一个隐函数 要求导数dy/dx 只要在这函数两边同时对x求导就可以了 最后再整理出dy/dx 如果有个实例就更好说了 有不懂欢迎追问

危彼薛2919那:x+y+lny=0也是隐函数?
弓沫群13988312935 ______ 当然是隐函数,因为y是由x+y+lny=0确定的

危彼薛2919e^(xy)+sin(x+y)+1=0 隐函数求导 -
弓沫群13988312935 ______ e^(xy)+sin(x+y)+1=0 [e^(xy)]'+[sin(x+y)]'+1'=0' e^(xy)*(xy)'+cos(x+y)*(x+y)'+0=0 e^(xy)(x'y+xy')+cos(x+y)*(x'+y')=0 e^(xy)(y+xy')+cos(x+y)(1+y')=0 ye^(xy)+xe^(xy)y'+cos(x+y)+cos(x+y)y'=0 [xe^(xy)+cos(x+y)]y'=-ye^(xy)-cos(x+y) y'=[-ye^(xy)-cos(x+y)]/[xe^(xy)+cos(x+y)]

危彼薛2919隐函数对x求导,为什么也对Y求导?比如x^2+xy+y^2=4,左右求导为什么是2x+y+xy'+2yy'=0不是2x+y+y^2=0 -
弓沫群13988312935 ______[答案] 因为其实y是x的函数,就是说y=y(x),所以也要导

危彼薛2919详细介绍x+y+z - 2√xyz隐函数z的偏导数 -
弓沫群13988312935 ______ 要是方程才可能确定隐函数的.应该是 x+y+z-2√xyz = 0 吧?对方程求微分,得 dx+dy+dz-(1/√xyz)(yzdx+xzdy+xydz) = 0,整理成 dz = (Dz/Dx)dx+(Dz/Dy)dy,的形式(留给你),即得 Dz/Dx = …,Dz/Dy =….

危彼薛2919大学微积分 求导数求下列隐函数的导数 x的2/3次方+y的2/3次方等于a的2/3次方 arctan(y/x)等于ln根号下(x的平方+y的平方) -
弓沫群13988312935 ______[答案] x^(2/3)+y^(2/3)=a^(2/3)2/3x^(-1/3)+2/3y^(-1/3)*y'=0y'=-(x/y)^(1/3)arctan(y/x)=ln(x^2+y^2)^(1/2)1/(1+(y/x)^2) * (y'x-y)/(x^2=1/2 *1/(x^2+y^2) * (2x+2yy')x^2/(x^2+y^2) *(y'x-y)/x^2=(x+yy')/(x^2+y^2)(y'x...

危彼薛2919求隐函数x^2+xy+y^2=4的导数y' -
弓沫群13988312935 ______[答案] 隐函数x^2+xy+y^2=4的导数y',两边同时求导就好了~ 两步就做完的题目,我实在不知你要的详细是什么意思~ 2x+y+x*y'+2y*y'=0 y'=-(2x+y)/(x+2y)

危彼薛2919z=yln(xy),求(d^3z)/(dxdy^2) z=1/y对x求导,结果是不存在吗z=yln(xy),求(d^3z)/(dxdy^2) -
弓沫群13988312935 ______[答案] z'x=y/(xy)* y=y/x z＂xy=1/x z＂'xyy=0 (d^3z)/(dxdy^2)=z＂'xyy=0