How do you differentiate g(x)=(3x-1)/(2x+1)?

May 6, 2018

I tried this:

Explanation:

We could use the Quotient Rule; given a function as:

$f \left(x\right) = g \frac{x}{h \left(x\right)}$

the derivative will be:

$f ' \left(x\right) = \frac{g ' \left(x\right) h \left(x\right) - g \left(x\right) h ' \left(x\right)}{h \left(x\right)} ^ 2$

$g ' \left(x\right) = \frac{3 \left(2 x + 1\right) - 2 \left(3 x - 1\right)}{2 x + 1} ^ 2$
$g ' \left(x\right) = \frac{\cancel{6 x} + 3 \cancel{- 6 x} + 2}{2 x + 1} ^ 2 = \frac{5}{2 x + 1} ^ 2$