复合函数y=ln(x-根号下x^2-1)求导

2024-12-03 03:39:03
推荐回答(2个)
回答1:

y=ln(x- √(x^2-1))
y' =[1/(x- √(x^2-1))]. d/dx (x- √(x^2-1))
=[1/(x- √(x^2-1))]. (1- x/√(x^2-1) )
= -1/√(x^2-1)

回答2:

y'=1/[x-√(x^2-1)] × [1-x/√(x^2-1)]
=1/[x-√(x^2-1)] × [(√(x^2-1)-x)/√(x^2-1)]
=-1/√(x^2-1)