y=In(x+根号下(x^2+1))求导数

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y=In(x+根号下(x^2+1))求导数
y=In(x+根号下(x^2+1))求导数

y=In(x+根号下(x^2+1))求导数
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)

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))

=根号下(x^2+1)分之1