Express $$ \frac{4x-1}{2(x-1)} - \frac{3}{2(x-1)(2x-1)} $$ as a single fraction in its simplest form - Edexcel - A-Level Maths Pure - Question 4 - 2011 - Paper 4

To differentiate $f(x) = \frac{3}{2x-1}$, we use the quotient rule:

Let:

• $u = 3$
• $v = 2x - 1$ Then:
• $u' = 0$
• $v' = 2$

According to the quotient rule:

$f'(x) = \frac{u'v - uv'}{v^2} = \frac{0(2x-1) - 3(2)}{(2x-1)^2} = \frac{-6}{(2x-1)^2}$

Now substituting $x=2$:

$f'(2) = \frac{-6}{(2(2)-1)^2} = \frac{-6}{(4-1)^2} = \frac{-6}{3^2} = \frac{-6}{9} = -\frac{2}{3}$