Hello dojo Originally Posted by
dojo 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
Yes, you'll need to use both the quotient and the product rules:$\displaystyle f(x) = \frac{1+xe^x}{1-xe^x}$
$\displaystyle \Rightarrow f'(x)= \frac{(1-xe^x)(xe^x+e^x)-(1+xe^x)(-xe^x-e^x)}{(1-xe^x)^2}$ $\displaystyle = \frac{e^x(1-xe^x)(x+1)+e^x(1+xe^x)(x+1)}{(1-xe^x)^2}$
$\displaystyle = \frac{e^x(x+1)(1-xe^x+1+xe^x)}{(1-xe^x)^2}$
$\displaystyle = \frac{2e^x(x+1)}{(1-xe^x)^2}$
Does that look about right?
Grandad