1. ## Differenciation Help needed.

i need to differenciate :

$\displaystyle x^3(2x+6)^4$ using product rule

i got to this stage :
$\displaystyle x^3 \times 8(2x+6)^3 + (2x+6)^4 \times 3x^2$

but the answer stated in the textbook is $\displaystyle 2x^2(2x+6)^3(7x+9)$
I think its the simplifying which i don't understand provided that the stage i got to is correct.
any help is appreichated.

Thank You

2. It is just rearranged.

Factorise the expression that you got.

--

Careful... don't forget the chain rule.

3. sorry i still don't understand do you mind please showing me exactly how it is done.

thanks

Kind Regards

4. $\displaystyle 8x^3(2x + 6)^3 + 3x^2(2x + 6)^4$

Take out $\displaystyle x^2$...

$\displaystyle x^2 ( 8x(2x + 6)^3 + 3(2x + 6)^4 )$

Next, factor out $\displaystyle (2x + 6)^3$...

$\displaystyle ( x^2 (2x + 6)^3 ) ( 8x + 3(2x + 6) )$

$\displaystyle ( x^2 (2x + 6)^3 ) ( 8x + 6x + 18)$

$\displaystyle ( x^2 (2x + 6)^3 ) ( 14x + 18 )$

Grab a 2 out of there...

$\displaystyle 2x^2 (2x + 6) (7x + 9)$

-Scott