Differenciation Help needed.

**rpatel** · September 20th 2007, 09:26 AM

i need to differenciate :

$<br /> x^3(2x+6)^4<br />$ using product rule

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

but the answer stated in the textbook is $2x^2(2x+6)^3(7x+9)$
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

**Krizalid** · September 20th 2007, 09:50 AM

It is just rearranged.

Factorise the expression that you got.

--

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

**rpatel** · September 20th 2007, 09:52 AM

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

thanks

Kind Regards

**ScottO** · September 20th 2007, 03:27 PM

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

Take out $x^2$ ...

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

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

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

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

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

Grab a 2 out of there...

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

-Scott

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