# How do you differentiate f(x)= (4x-4) / (4x+4) using the quotient rule?

Nov 19, 2015

$\setminus \frac{16}{16 {x}^{2} + 32 x + 16}$

#### Explanation:

Quotient rule: if you have to differentiate a function of the form

$\setminus \frac{g \left(x\right)}{h \left(x\right)}$, then the derivative is

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

Let's compute the single quantities:

• $g \left(x\right) = 4 x - 4$
• $g ' \left(x\right) = 4$
• $h \left(x\right) = 4 x + 4$
• $h ' \left(x\right) = 4$
• ${h}^{2} \left(x\right) = {\left(4 x + 4\right)}^{2}$

Plugging these into the formula gives

$\setminus \frac{4 \left(4 x + 4\right) - 4 \left(4 x - 4\right)}{{\left(4 x + 4\right)}^{2}} = \setminus \frac{16}{16 {x}^{2} + 32 x + 16}$