# Question e9a58

##### 2 Answers
Apr 12, 2017

color(blue)(x^3+2x^2+3x+6

#### Explanation:

$\left(x + 1\right) \left({x}^{2} + 3\right)$

$\textcolor{w h i t e}{a a a a a a a a a a a a a}$${x}^{2} + 3$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$$x + 1$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- - - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a}$${x}^{3}$$\textcolor{w h i t e}{a a a a}$$+ 3 x$
$\textcolor{w h i t e}{a a a a a a a a a a a a a a a a a}$$2 {x}^{2}$$\textcolor{w h i t e}{a a a a}$$+ 6$
$\textcolor{w h i t e}{a a a a a a a a a a a a a}$$- - - - - -$
$\textcolor{w h i t e}{a a a a a a a a a a a a}$color(blue)(x^3+2x^2+3x+6

Apr 12, 2017

$3 {x}^{2} + 4 x + 3$

#### Explanation:

$\text{Expand the brackets}$

$\left(x + 2\right) \left({x}^{2} + 3\right) = {x}^{3} + 2 {x}^{2} + 3 x + 6$

differentiate each term using the $\textcolor{b l u e}{\text{power rule}}$

• d/dx(ax^n)=nax^(n-1)#

$\Rightarrow \frac{d}{\mathrm{dx}} \left({x}^{3} + 2 {x}^{2} + 3 x + 6\right)$

$= 3 {x}^{2} + 4 x + 3$