cos(xy)=x-y所确定的隐函数y=y(x)的导数dy/dx
题目
cos(xy)=x-y所确定的隐函数y=y(x)的导数dy/dx
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答案
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...
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