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

1. ## 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?

2. ## Re: Find g'(x) and g"(x)

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:
Write your first derivative as:
$\displaystyle g'(x) = \frac{x - 1}{x^2} \cdot e^x = \frac{1}{x} \cdot e^x - \frac{1}{x^2} \cdot e^x$

and try it again.

-Dan

3. ## Re: Find g'(x) and g"(x)

I was able to find the second derivative after a third try.