cos(xy)=x－y所确定的隐函数y=y(x)的导数dy/dx快
问题描述：
cos(xy)=x－y所确定的隐函数y=y(x)的导数dy/dx
快
答
F(x,y)=cos(xy)-x+y,
dy/dx=-F'x/F'y=-(-ysin(xy)-1)/(-xsin(xy)+1)
答
cos(xy)=x-y,隐函数,两边求导-sin(xy)*(xy)'=1-y'-sin(xy)*(y+xy')=1-y'-ysin(xy)-xcos(xy)*y'=1-y'y'[1-xsin(xy)]=1+ysin(xy)y'=[1+ysin(xy)]/[1-xsin(xy)]也可用设二元函数f(x,y)=cos(xy)-x+y用隐函数求导法:f'x(x...