设函数y=f((x+1)/(x-1))，其中f(x)满足f'(x)=arctan√x，则dy/dx|x=2=()

设函数y=f((x+1)/(x-1))，其中f(x)满足f'(x)=arctan√x，则dy/dx|_x=2=()
A、arctan√2
B、-(2π/3)
C、2π/3
D、π/3
【正确答案】：B
【题目解析】：复合函数的求导法则．因为f'(x)=arctan√x，所以dy/dx=f'((x+1)/(x-1))•((x+1)/(x-1))'=f'((x+1)/(x-1))•[-2/(x-1)²]=-2arctan√[(x+1)/(x-1)]/(x-1)²，则dy/dx|_x=2=-2arctan√3=-(2/3)π．