一道求微分的题目
问题描述:
一道求微分的题目
y=x/根号(x平方+1)
微分是多少,
答
因为y=x/√[(x^2)+1]
所以:
dy={√[(x^2)+1]-(x^2)/{[(x^2)+1]^(3/2)}}dx/[(x^2)+1]
={{[(x^2)+1]^2-x^2}/[(x^2)+1]^(3/2)}dx/[(x^2)+1]
={(x^4+x^2+1)/[(x^2)+1]^(3/2)}dx/[(x^2)+1]
=(x^4+x^2+1)/{[(x^2)+1]^2}
=[(x^4+x^2+1)/(x^4+2x^2+1)]dx