How to Begin Differentiating Products with x^2(x+1)(x-2)^7?

[footprints]

x^2(x+1)(x-2)^7
Could someone show me how to start?

 

[Benny]

Well you currently have a product of three functions. I suggest starting by 'combining' the first two parts of the product as follows.

<br /> \frac{d}{{dx}}\left[ {x^2 \left( {x + 1} \right)\left( {x - 2} \right)^7 } \right] = \frac{d}{{dx}}\left[ {\left( {x^3 + x^2 } \right)\left( {x - 2} \right)^7 } \right]<br />

Now just use the product rule to differentiate it.

 

[footprints]

Ah! I thought so to. But just wasn't sure. Thanks! Hapyy new year!

 

[dextercioby]

In this simple case it works,as u're,mutiplying two simple polynomials.But what if thepolynomials had 50 terms?Would u do 2500 multiplications?
Here's the deal:the Leibniz rule is very general.It can be easily extended to finite arbitrary number of factors:
(ABC...Z)&#039;=A&#039;BC...Z+AB&#039;C...Z+ABC&#039;...Z+...+ABC...Z&#039;
In your case,there are only 3 very simple polynomials.If u want to,u may not make the multiplications after the differentiation.

Daniel.

EDIT:'Prime' denotes differentiation.

 

[footprints]

Just checking, A&#039; is what I get after I differentiate A right?

 

[Nylex]

Just checking, A&#039; is what I get after I differentiate A right?

Yes it is.

 

[footprints]

Thanks Nylex! Happy New Year!