Hi - I just can't seem to get this one right. Looking to get the first derivative...

(1 + xe^x)/(1 - xe^x)

I assume that you use the quotient rule but I end up in a mess.

Could someone please talk me thorugh this one?

Thanks, D

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- Mar 7th 2010, 09:18 AMdojo[SOLVED] Tricky Diff question
Hi - I just can't seem to get this one right. Looking to get the first derivative...

(1 + xe^x)/(1 - xe^x)

I assume that you use the quotient rule but I end up in a mess.

Could someone please talk me thorugh this one?

Thanks, D - Mar 7th 2010, 09:29 AMGrandad
Hello dojoYes, you'll need to use both the quotient and the product rules:

$\displaystyle f(x) = \frac{1+xe^x}{1-xe^x}$Does that look about right?

$\displaystyle \Rightarrow f'(x)= \frac{(1-xe^x)(xe^x+e^x)-(1+xe^x)(-xe^x-e^x)}{(1-xe^x)^2}$$\displaystyle = \frac{e^x(1-xe^x)(x+1)+e^x(1+xe^x)(x+1)}{(1-xe^x)^2}$

$\displaystyle = \frac{e^x(x+1)(1-xe^x+1+xe^x)}{(1-xe^x)^2}$

$\displaystyle = \frac{2e^x(x+1)}{(1-xe^x)^2}$

Grandad

- Mar 8th 2010, 04:37 AMdojo
The book gives the answer with the same numerator as you have bu the denom as (xe^2 - 1)^2

Thanks for the workings - I think my algebra needs a bit of work. I think the book must be wrong as the quotien rule does state that v^2 is the denom.

Thanks - Mar 8th 2010, 06:00 AMGrandad
- Mar 8th 2010, 06:30 AMdojo
My typo!! thanks for the reply(Happy)