Question

If y=log⁡(^x⁄(x^2 – 1)), then nth derivative of y is ?

(a) (-1)^(n-1) (n-1)!(x^(-n) + (x-1)^(-n) + (x+1)^(-n))

(b) (-1)^n (n)! (x^(-n-1) + (x-1)^(-n-1) + (x+1)^(-n-1))

(c) (-1)^(n+1) (n+1)!(x^(-n) + (x-1)^(-n) + (x+1)^(-n))

(d) (-1)^n(n)! (x^(-n-1) + (x-1)^(-n+1) + (x+1)^(-n+1))

I got this question during a job interview.

I'd like to ask this question from The nth Derivative of Some Elementary Functions topic in portion Differential Calculus of Engineering Mathematics

Answer 1

The correct answer is (a) (-1)^(n-1) (n-1)!(x^(-n) + (x-1)^(-n) + (x+1)^(-n))

To explain: Y=log(x) – log(x^2 – 1)

y1 = x^(-1)-2x/(x^2-1)

y1 = x^(-1)-(x-1)^(-1) + (x+1)^(-1)

yn = (-1)^(n-1) (n-1)!(x^(-n)-(x-1)^(-n) + (x+1)^(-n)).