Question

whats the 2nd derivative of f(x) = 3x-2/(x-1)^2

Answer 1

f'(x)=[3(x-1)^2-(3x-2)2(x-1)]/(x-1)^4
=(x-1)[3(x-1)-2(3x-2)]/(x-1)^4
=[3x-3-6x+4]/(x-1)^3
=-3x+1/(x-1)^3
f''(x)=-3(x-1)^3-(-3x+1)6(x-1)/(x-1)^6
=(x-1)[-3(x-1)^2-6(-3x+1)]/(x-1)^6
=-3(x^2+1-2x)+18x-6/(x-1)^5
=-3x^2-3+6x+18x-6/(x-1)^5
=-3x^2+24x-9/(x-1)^5