# How do you find the derivative of x(x-4)^3?

May 25, 2018

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

#### Explanation:

Using the product rule:

$\frac{d}{\mathrm{dx}} \left[x {\left(x - 4\right)}^{3}\right] = x \frac{d}{\mathrm{dx}} \left[{\left(x - 4\right)}^{3}\right] + \left[\frac{d}{\mathrm{dx}} \left(x\right)\right] {\left(x - 4\right)}^{3}$

$\frac{d}{\mathrm{dx}} \left[x {\left(x - 4\right)}^{3}\right] = 3 x {\left(x - 4\right)}^{2} + {\left(x - 4\right)}^{3}$

$\frac{d}{\mathrm{dx}} \left[x {\left(x - 4\right)}^{3}\right] = {\left(x - 4\right)}^{2} \left(3 x + x - 4\right)$

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