gotta find the first and second derivative of f(x)=x^2/(x-1)

Question

thanks for help!

Answer 1

quotient rule:

f' = ((2x)(x-1) - (x^2)(1))/(x-1)^2
= x(x-2)/(x-1)^2

f'' = 2/(x-1)^3

Or, divide first:

f = x^2/(x-1) = x+1 + 1/(x-1)
f' = 1 - 1/(x-1)^2
f'' = 2/(x-1)^3