What is the derivative of -2/(2x-4)^2?

Mar 1, 2017

$\frac{d}{\mathrm{dx}} - \frac{2}{2 x - 4} ^ 2 = \frac{1}{x - 2} ^ 3$

Explanation:

$\frac{d}{\mathrm{dx}} - \frac{2}{2 x - 4} ^ 2 = \frac{d}{\mathrm{dx}} - \frac{2}{{\left(2 \left(x - 2\right)\right)}^{2}}$
$\text{ } = \frac{d}{\mathrm{dx}} - \frac{2}{4 {\left(x - 2\right)}^{2}}$
$\text{ } = \frac{d}{\mathrm{dx}} - \frac{1}{2} {\left(x - 2\right)}^{- 2}$

So applying the power rule we get;

$\frac{d}{\mathrm{dx}} - \frac{2}{2 x - 4} ^ 2 = - \frac{1}{2} \left(- 2\right) {\left(x - 2\right)}^{- 3}$
$\text{ } = 1 {\left(x - 2\right)}^{- 3}$
$\text{ } = \frac{1}{x - 2} ^ 3$