y=(3-3/4x^2)^(1/2)的导数为什么是-3x/[4*(3-3/4x^2)^(1/2)]而不是-1/[2*(3-3/4x^2)^(1/2)]
问题描述:
y=(3-3/4x^2)^(1/2)的导数为什么是-3x/[4*(3-3/4x^2)^(1/2)]而不是-1/[2*(3-3/4x^2)^(1/2)]
答
y'=[(3-3/4x^2)^(1/2)]'
=1/2*(3-3/4x^2)^(1/2-1)*(3-3/4x^2)' 利用复合函数求导法则,3-3/4x^2是中间变量
=1/2*(3-3/4x^2)^(-1/2)*(-3/4 *2x)'
=-3x/4*(3-3/4x^2)^(-1/2)