Question

obtain nth derivative for y=(2x+1)/(x-1)(2x+1)

Answer 1

x-1

Answer 2

The numerator increases exponentially as n increases:
http://www.wolframalpha.com/input/?i=1000th++derivative+y%3D%282x%2B1%29%2F%28x-1%29%282x%2B1%29
http://www.wolframalpha.com/input/?i=1000th++derivative+y%3D%282x%2B1%29%2F%28x-1%29%282x%2B1%29

Answer 3

However, the denominator is predictable.

Answer 4

same...if n is odd..then derivative will be -1/(x-1)^2
if n is even then derivative is = 1/(x-1)^2