y=根号下x^2+1的微分怎么求.

题目

y=根号下x^2+1的微分怎么求.

答案

∵y=√(x²+1)
∴dy=d(√(x²+1))
=(√(x²+1))'dx
=(1/2)(x²+1)'/[√(x²+1)]dx
=(1/2)(2x)/[√(x²+1)]dx
=xdx/[√(x²+1)].