曲线sin(xy)+ln(y-x)=x在点(0,1)处的切线方程?

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曲线sin(xy)+ln(y-x)=x在点(0,1)处的切线方程?
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曲线sin(xy)+ln(y-x)=x在点(0,1)处的切线方程?
曲线sin(xy)+ln(y-x)=x在点(0,1)处的切线方程?

曲线sin(xy)+ln(y-x)=x在点(0,1)处的切线方程?
对x求导
cos(xy)*(xy)'-1/(y-x)*(y-x)'=1
cos(xy)*(y+x*y')-(y'-1)/(y-x)=1
y*cos(xy)+xcos(xy)*y'-y'/(y-x)+1/(y-x)=1
y'=[1-1/(y-x)-y*cos(xy)]/(xcos(xy)-1/(y-x)]
x=0,y=1
所以斜率k=y'=-1/(-1)=1
所以x-y+1=0