# How do you find the derivative of 1/3 (x^2-3x-5) * (2x-3)?

May 7, 2018

$2 {x}^{2} - 6 x - \frac{1}{3}$

#### Explanation:

$\text{differentiate using the "color(blue)"power rule}$

•color(white)(x)d/dx(ax^n)=nax^(n-1)

$\text{expand factors and distribute}$

$= \frac{1}{3} \left(2 {x}^{3} - 9 {x}^{2} - x + 15\right)$

$= \frac{2}{3} {x}^{3} - 3 {x}^{2} - \frac{1}{3} x + 5$

$\frac{d}{\mathrm{dx}} \left(\frac{2}{3} {x}^{3} - 3 {x}^{2} - \frac{1}{3} x + 5\right)$

$= 2 {x}^{2} - 6 x - \frac{1}{3}$