1. ## Product Rule

Hi,

First sorry if this is the wrong forum!

I'm following along with an example of the product rule in my text book but i can't tell how they've got form one step to another.

The question is: $\displaystyle (x+1)^3(2x-5)^2$

Eventually they go from this:
$\displaystyle ((2x-5)^2)(3(x+1)^2) + ((x+1)^3)(2(2)(2x-5))$

To this:

$\displaystyle (2x-5)(x+1)^2(3(2x-5)+4(x+1))$

And i can't tell how they've done that. I you could help at all it'd be a great help.

2. Originally Posted by aceband
Hi,

First sorry if this is the wrong forum!

I'm following along with an example of the product rule in my text book but i can't tell how they've got form one step to another.

The question is: $\displaystyle (x+1)^3(2x-5)^2$

Eventually they go from this:
$\displaystyle ((2x-5)^2)(3(x+1)^2) + ((x+1)^3)(2(2)(2x-5))$

To this:

$\displaystyle (2x-5)(x+1)^2(3(2x-5)+4(x+1))$

And i can't tell how they've done that. I you could help at all it'd be a great help.

$\displaystyle (x+1)^3(2x-5)^2$

They used the chain rule when differentiating $\displaystyle (2x-5)^2$

$\displaystyle \frac{d}{dx}(2x-5)^2 = 2(2x-5) \times 2$

3. Brilliant - makes more sense now.

I still can't work out how they've gone from one line to the next thought. Lots of changes in powers and new integers cropping up?

4. Wait! Think i see now! Is it that they are taking out a factor of $\displaystyle (2x-5)(x+1)^2$

?