1、设函数y=y(x)由方程e^x-e^y=sin(xy)所确定,求(dy/dx)|x=0；2、设函数f(x)=x^2+(1/x)+1则f'(x)=?

1) x=0代入方程：1-e^y=0,得y(0)=0
两边对X求导：e^x-y'e^y=cos(xy)(y+xy')
y'=[e^x-ycos(xy)]/[xcos(xy)+e^y]
代入x=0,y(0)=0,故y'(0)=1
2)f'(x)=2x-1/x^2