求导y=2x/(x-1)² 曲线y=2/x²+1在点P(1,1)处的切线方程是

问题描述:

求导y=2x/(x-1)² 曲线y=2/x²+1在点P(1,1)处的切线方程是

y=2x/(x-1)²
y'=[2(x-1)²-2x*2(x-1)]/(x-1)^4
=(2x²-4x+2-4x²+2x)/(x-1)^4
=(-2x²-2x+2)/(x-1)^4
=-2(x²+x-1)/(x-1)^4
y=2/x²+1
k=y'=2*(-2)x^(-3)+1
当x=1时,k=4+1=5
设切线方程为:y=5x+m
切线过(1,1),则m=-4
所以曲线y=2/x²+1在点P(1,1)处的切线方程是:y=5x-4