Find the equation of the tangent line at x=2 for f(x)=√(（4x+1)/(5x-1))

题目

Find the equation of the tangent line at x=2 for f(x)=√(（4x+1)/(5x-1))
100分题,

答案

定义域为D={x|x=1/5}
导数f'(x) =-9/[2*（5x-1)²*√(（4x+1)/(5x-1)) ]
f'(2)=-1/18
f(2)=1
在点（2,1）,函数的切线的斜率为-1/18,切线方程为 y-1=-1/18 *(x-2)
整理,得 x+18y -20=0