Question

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

Answer 1

`\frac{16}{16x^2+32x+16}`

Explanation:

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

`\frac{g(x)}{h(x)}`, then the derivative is

`\frac{g'(x)h(x)-g(x)h'(x)}{h^2(x)}`

Let's compute the single quantities:

• `g(x)=4x-4`
• `g'(x)=4`
• `h(x)=4x+4`
• `h'(x)=4`
• `h^2(x)=(4x+4)^2`

Plugging these into the formula gives

`\frac{4(4x+4) - 4(4x-4)}{(4x+4)^2} = \frac{16}{16x^2+32x+16}`