# How do you find the derivative of  (2x-1)^3?

Aug 17, 2016

$\frac{\mathrm{dy}}{\mathrm{dx}} = 6 {\left(2 x - 1\right)}^{2}$

#### Explanation:

a simple technique to consider is using the chain rule
which states

$\frac{\mathrm{dy}}{\mathrm{dx}} = \frac{\mathrm{dy}}{\mathrm{du}} \cdot \frac{\mathrm{du}}{\mathrm{dx}}$

here $y = {\left(2 x - 1\right)}^{3} \mathmr{and} u = 2 x - 1$

$\frac{\mathrm{du}}{\mathrm{dx}} = 2$

$\frac{\mathrm{dy}}{\mathrm{du}} = 3 {\left(u\right)}^{2}$

now we can also just not replace the $u$ so

$\frac{\mathrm{dy}}{\mathrm{du}} = 3 {\left(2 x - 1\right)}^{2}$

now we can solve
$\frac{\mathrm{dy}}{\mathrm{dx}} = 6 {\left(2 x - 1\right)}^{2}$