Question

If y=^x^4⁄x^2-1, then?

(a) 0.5*(-1)^n (n-1)! [(x-1)^-n-1 + (x+1)^-n-1]

(b) 0.5*(-1)^n (n-1)! [x^– n-1 + (x-1)^-n-1 + (x+1)^-n-1]

(c) 0.5*(-1)^n (n-1)! [(x-1)^-n + (x+1)^-n)]

(d) 0.5*(-1)^n (n-1)! [x^-n + (x-1)^-n + (x+1)^-n]

I got this question by my school principal while I was bunking the class.

The origin of the question is The nth Derivative of Some Elementary Functions in section Differential Calculus of Engineering Mathematics

Answer 1

Correct option is (a) 0.5*(-1)^n (n-1)! [(x-1)^-n-1 + (x+1)^-n-1]

The best explanation: \(y = x^2+\frac{x^2}{x^2-1}\)

\(y = x^2+\frac{1}{x^2-1}\)+1

\(y = x^2+1+\frac{1}{(x-1)(x+1)}\)

\(y = x^2+1+0.5[\frac{1}{(x-1)}-\frac{1}{(x+1)}]\)

\(y_n=0.5*(-1)^n (n-1)![(x-1)^{-n-1}+(x+1)^{-n-1}]\)