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
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![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](/uploads/image/z/10196169-33-9.jpg?t=%E6%B1%82%E5%AF%BCy%3D2x%2F%28x-1%29%26%23178%3B+%E6%9B%B2%E7%BA%BFy%3D2%2Fx%26%23178%3B%2B1%E5%9C%A8%E7%82%B9P%EF%BC%881%2C1%EF%BC%89%E5%A4%84%E7%9A%84%E5%88%87%E7%BA%BF%E6%96%B9%E7%A8%8B%E6%98%AF)
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
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
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
(1)Y′=(2-2X2)/(X-1)4
(2)Y=-4X+5