# Find g'(x) and g"(x)

• Sep 29th 2013, 06:36 PM
nycmath
Find g'(x) and g"(x)
I need to find the first and second derivative of
g(x) = (e^x)/x.

I found g'(x) to be e^x(x-1)/(x^2).

I then found g"(x) to be (e^x)/x^3 but the book's answer is more involved.

According to the book, the complete answer is
(e^x)/(x^3) times (x^2-2x+2).

Where does the trinomial come from?
• Sep 29th 2013, 07:09 PM
topsquark
Re: Find g'(x) and g"(x)
Quote:

Originally Posted by nycmath
I need to find the first and second derivative of
g(x) = (e^x)/x.

I found g'(x) to be e^x(x-1)/(x^2).

I then found g"(x) to be (e^x)/x^3 but the book's answer is more involved.

According to the book, the complete answer is
(e^x)/(x^3) times (x^2-2x+2).

Where does the trinomial come from?

Without seeing your work I can only guess. However it's probably here:
$g'(x) = \frac{x - 1}{x^2} \cdot e^x = \frac{1}{x} \cdot e^x - \frac{1}{x^2} \cdot e^x$