y=x/✔(1-x^2)的复合函数的导数_数学解答

y=x/✔(1-x^2)的复合函数的导数

人气：436 ℃　时间：2019-10-19 06:03:59

解答

y = x/√(1-x^2)
y' = [√(1-x^2) + 0.5*2x^2/√(1-x^2)]/(1-x^2)
= [√(1-x^2) + x^2/√(1-x^2)]/(1-x^2)
= [(1-x^2) + x^2]/(1-x^2)^(2/3)
= 1 / (1-x^2)^(2/3)