哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?

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哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?

哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?
哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?

哪个是曲线Y=x/x+2在点(-1,-1)处的切线方程?是Y=2x+1还是Y=-2x-3?
y=x/(x+2)=(x+2-2)/(x+2)=1-2/(x+2)
求导y'=2/(x+2)^2
切线斜率K=y'=2/(-1+2)^2=2
方程y+1=2(x+1),即y=2x+1

y=x/(x+2)=1-2/(x+2)
y'= 2/(x+2)^2
y'(-1)= 2/(-1+2)^2=2
曲线 y=x/(x+2)在点(-1,-1)处的切线方程为:
y-(-1)=2(x-(-1) -->
y=2x+1

y=x/(x+2)
y'=[(x+2)-x]/(x+2)^2=2/(x+2)^2=2
所以
y+1=2(x+1)=2x+2
y=2x+1