求由方程x^2 2xy-y^2=5所确定的隐函数y=y(x)的微分dy及导数
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![求由方程x^2 2xy-y^2=5所确定的隐函数y=y(x)的微分dy及导数](/uploads/image/f/5746173-69-3.jpg?t=%E6%B1%82%E7%94%B1%E6%96%B9%E7%A8%8Bx%5E2+2xy-y%5E2%3D5%E6%89%80%E7%A1%AE%E5%AE%9A%E7%9A%84%E9%9A%90%E5%87%BD%E6%95%B0y%3Dy%28x%29%E7%9A%84%E5%BE%AE%E5%88%86dy%E5%8F%8A%E5%AF%BC%E6%95%B0)
xy+e^y=y+1(1)求d^2y/dx^2在x=0处的值:(1)两边分别对x求导:y+xy'+e^yy'=y'y/y'+x+e^y=1(2)(2)两边对x再求导一次:(y'y'-yy'')/y'^
左右对x求导有y'/y=sec²(xy)(y+xy')整理有y'=y²/(cos(xy)-xy)所以dy=(y²/(cos(xy)-xy))dx
隐函数求导设z=x²y²-cos(xy)dy/dx=-(δz/δx)/(δz/δy)=-(2xy²+ysin(xy))/(2x²y+xsin(xy))=-y/x
-sin(xy)[ydx+xdy]=2xy^2*dx+x^2*2ydy-sin(xy)ydx-sin(xy)xdy=2xy^2*dx+2x^2*ydy-2x^2*ydy-sin(xy)xdy=2xy^
这是一个复合函数求导,y=y(x)所以求e^y的导数首先对整体求导,再对y求导即为e^y*y'xy的导数为y+x*y'(根据求导规则)所以两边求导可得e^y*y'-y-x*y'=0
直接在等式中零,x=0,y=y(0),可得关于y(0)的方程解出y(0)即可.具体:e^0*y(0)+lny(0)/1=0即-y(0)=lny(0)作图y1=-x,y2=ln(x),两者的交点的横坐标
把x=0代入原方程得0+e^0+y=2∴y=1方程两边对x求导得:y+xy'+e^(xy)(y+xy')+y'=0移项、整理得:[x+xe^(xy)+1]y'=y+ye^(xy)∴y'=[y+ye^(
e^(xy)+sin(xy)=y(y+xy')e^(xy)+(y+xy')cos(xy)=y'y'=(ye^(xy)+ycos(xy))/(1-xe^(xy)-xcos(xy))
两边同时对X求导y+xy`=e^x+y`y`=(e^x-y)/(x-1)
这个题目要利用隐函数的求导法则.则sin(x^2+y)=xy(两边同时求导,还要结合复合函数的求导法则)cos(x^2+y)*(2x+y′)=y+xy′2xcos(x^2+y)-y=xy′-y′cos
两边对x求导得y+xy'=(1+y')/(x+y)y(x+y)+x(x+y)y'=1+y'y'[x(x+y)-1]=1-y(x+y)y'=[1-y(x+y)]/[x(x+y)-1]dy=[1-y(x+
在xy+e^xy+y=e两边同时进行取微分,ydx+xdy+e^xy*(ydx+xdy)+dy=0然后求出dy/dx求出来后,在dy/dx等式两边两边同时求导,求导的过程中会有dy/dx,带入第一步求
直接求导,用xy表示导数【欢迎追问,
对y^2-2xy=7求微分,得2ydy-2(ydx+xdy)=0,∴(y-x)dy=ydx,∴dy/dx=y/(y-x).
设dy/dx=y'.求导,2yy'-2y-2xy'=0dy/dx=y'=y/(y-x)
x=0时,代入方程得:1+1=y,得:y=2对x求导:(y+xy')e^xy-sin(xy)*(y+xy')=y'将x=0,y=2代入得:2=y'故dy(0)=2dx
/>e^y+xy+e^x=0两边同时对x求导得:e^y·y'+y+xy'+e^x=0得y'=-(y+e^x)/(x+e^y)y''=-[(y'+e^x)(x+e^y)-(y+e^x)(1+e^y·y'
dy/dx=-fx/fy,你自己可以算吧
两边对x求导xy^2+sinx=e^yy^2+2xyy'+cosx=e^y*y'y'(e^y-2xy)=y^2+cosxy'=(y^2+cosx)/(e^y-2xy)