y=In(x+根号下(x^2+1))求导数

问题描述:

y=In(x+根号下(x^2+1))求导数

=根号下(x^2+1)分之1

y'=[1/(x+根号下(x^2+1)) ]*(x+根号下(x^2+1))'
=[1/(x+根号下(x^2+1)) ]*(1+2x/根号下(x^2+1))

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