Differentiating this Expression

Can anyone help me with this? The question asks to differentiate the following...

(x-5)^8 * (x+3)^6

The way I attempted it was to try using the product rule, but I don't get the same answer as stated in the book.

I used the chain rule to differentiate each of the two arguments, getting 8(x-5)^7 and 6(x+3)^5 respectively. At that point I attempted to use the product rule, getting:

8(x-5)^7*(x+3)^6 + (x-5)^8*6(x+3)^5

but this is not the correct answer, unless there's some algebra I'm not seeing with the answer above - I suspect I'm doing something amiss. Any help is appreciated!

Re: Differentiating this Expression

Quote:

Originally Posted by

**YoungMarbleGiant** differentiate the following...

$\displaystyle (x-5)^8 * (x+3)^6$

I used the chain rule to differentiate each of the two arguments, getting 8(x-5)^7 and 6(x+3)^5 respectively. At that point I attempted to use the product rule, getting:

$\displaystyle 8(x-5)^7*(x+3)^6 + (x-5)^8*6(x+3)^5$

but this is not the correct answer

That answer is certainly correct. Why do you doubt it?

It can be factored: $\displaystyle (x-5)^7(x+3)^5[8(x+3)+6(x-5)]$

Re: Differentiating this Expression

Quote:

Originally Posted by

**Plato** That answer is certainly correct. Why do you doubt it?

It can be factored: $\displaystyle (x-5)^7(x+3)^5[8(x+3)+6(x-5)]$

I was sure the method was correct, but the answer in the exercise book is quite different. It gives the answer as $\displaystyle 2(7x-3)(x-5)^7(x+3)^5$.

I looked at ways of simplifying/factoring, but the $\displaystyle (7x-3)$ was throwing me off. Do you have any idea how to get to this answer from the point where I reached? Thank you.

Re: Differentiating this Expression

That's exactly what Plato said, because $\displaystyle [8(x+3)+6(x-5)]=(8x+24+6x-30)=14x-6=2(7x-3)$

Re: Differentiating this Expression

Alright, thanks to you both.