求导In(x+√(x^2+1)),其答案为1/√(x^2+1).求其运算过程.

Question

求导In(x+√(x^2+1)),其答案为1/√(x^2+1).求其运算过程.

Answer 1

y′=(1+2x/(2*√(x²+1))/(x+√(x²+1))
=[(x+√(x²+1))/√(x²+1)]/(x+√(x²+1))
= 1/√(x²+1)