1、设函数y=y(x)由方程e^x-e^y=sin(xy)所确定,求(dy⼀dx)|x=0;2、设函数f(x)=x^2+(1⼀x)+1则f✀(x)=?

2025-02-24 08:42:20
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回答1:

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