求导：y=ln（x+√（a^2+x^2））i need process and detailed steps if necessa_数学解答

求导：y=ln（x+√（a^2+x^2））
i need process and detailed steps if necessary.

人气：360 ℃　时间：2019-10-31 00:56:12

解答

y'=[1/(x+√(a^2+x^2))]*[x+√(a^2+x^2)]'
=[1/(x+√(a^2+x^2))]*[1+2x/2√(a^2+x^2)]
=[1/(x+√(a^2+x^2))]*[(√(a^2+x^2)+x)/√(a^2+x^2)]
=1/√(a^2+x^2)