cos(xy)=x－y所确定的隐函数y=y(x)的导数dy/dx
2个回答

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,y)+f,y(x,y)*y'=0

f'x(x,y)=-sin(xy)*(xy)'-1

=-ysin(xy)-1

f'y(x,y)=-sin(xy)*(xy)'+1

=-xsin(xy)+1

∴[-ysin(xy)-1]+[-xsin(xy)+1]*y'=0

y'=-[ysin(xy)-1]/[-xsin(xy)+1]

y'=[1+ysin(xy)]/[1-xsin(xy)]

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