Given function is in quotient form, so let us assume u(x) = x – 1 and v(x) = 2x.
Now, by quotient rule, the derivative of the given function becomes,
(d/dx) [u(x)/v(x)] = [u'(x) v(x) – u(x) v'(x)]/ [v(x)]^2
= [1(2x) – (x – 1)(2)]/(2x)^2
= (2x – 2x + 1)/4x^2
= 1/4x^2