求由方程cos(xy)=x^2*y^2所确定的函数y的微分有四个选项—y/x*dxy/x*dxx/y*dx—x/y*dx

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求由方程cos(xy)=x^2*y^2所确定的函数y的微分有四个选项—y/x*dxy/x*dxx/y*dx—x/y*dx

求由方程cos(xy)=x^2*y^2所确定的函数y的微分有四个选项—y/x*dxy/x*dxx/y*dx—x/y*dx
求由方程cos(xy)=x^2*y^2所确定的函数y的微分
有四个选项
—y/x*dx
y/x*dx
x/y*dx
—x/y*dx

求由方程cos(xy)=x^2*y^2所确定的函数y的微分有四个选项—y/x*dxy/x*dxx/y*dx—x/y*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
故dy=-y/xdx

zxcxzczxc

-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^2*dx+sin(xy)ydx
-[2x^2*y+sin(xy)x]dy=[2xy^2+sin(xy)y]dx
dy/dx=-[2xy^2+sin(xy)y]/[2x^2*y+sin(xy)x]