作业帮[根号(1-x²﹚]的导数是怎么算的,里面的数是怎么开出来的[(1-x^2)^0.5]'=0.5(1-x^2)^(0.5-1)×（1-x^2）'=-x/[(1-x^2)^0.5]第二步不懂
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/08 12:23:56
![[根号(1-x²﹚]的导数是怎么算的,里面的数是怎么开出来的[(1-x^2)^0.5]'=0.5(1-x^2)^(0.5-1)×（1-x^2）'=-x/[(1-x^2)^0.5]第二步不懂](/uploads/image/z/14775182-62-2.jpg?t=%5B%E6%A0%B9%E5%8F%B7%281-x%26%23178%3B%EF%B9%9A%5D%E7%9A%84%E5%AF%BC%E6%95%B0%E6%98%AF%E6%80%8E%E4%B9%88%E7%AE%97%E7%9A%84%2C%E9%87%8C%E9%9D%A2%E7%9A%84%E6%95%B0%E6%98%AF%E6%80%8E%E4%B9%88%E5%BC%80%E5%87%BA%E6%9D%A5%E7%9A%84%5B%281-x%5E2%29%5E0.5%5D%27%3D0.5%281-x%5E2%29%5E%280.5-1%29%C3%97%EF%BC%881-x%5E2%EF%BC%89%27%3D-x%2F%5B%281-x%5E2%29%5E0.5%5D%E7%AC%AC%E4%BA%8C%E6%AD%A5%E4%B8%8D%E6%87%82)
[根号(1-x²﹚]的导数是怎么算的,里面的数是怎么开出来的[(1-x^2)^0.5]'=0.5(1-x^2)^(0.5-1)×（1-x^2）'=-x/[(1-x^2)^0.5]第二步不懂
[根号(1-x²﹚]的导数是怎么算的,里面的数是怎么开出来的
[(1-x^2)^0.5]'=0.5(1-x^2)^(0.5-1)×（1-x^2）'=-x/[(1-x^2)^0.5]第二步不懂
[根号(1-x²﹚]的导数是怎么算的,里面的数是怎么开出来的[(1-x^2)^0.5]'=0.5(1-x^2)^(0.5-1)×（1-x^2）'=-x/[(1-x^2)^0.5]第二步不懂
这是一个复合函数
要一层一层求导
[根号(1-x²﹚]=(1-x^2)^1/2
[(1-x^2)^1/2]'=[(1-x^2)^1/2]'[1-x^2]'
=[1/2(1-x^2)^(1/2-1)][-2x]
=-x/[(1-x^2)^(1/2)]