Differentiate logarithm headache

[MrGinsu]

Hello,

I'm trying to figure out how to solve this differentiation problem. I'm sure the steps are staring me in the face, but I am missing some key step.

f(x) = (x^(1/2)) ln(x)

To me this looks like I should use the product rule and do something like:

[ 1/2 * 1/(x^(1/2)) * ln(x) ] + [(x^(1/2)) * 1/x]

But I don't know where to go from here

According to the back of the book, the answer is:

f'(x) = (2 + ln(x)) / (2x^(1/2))

Anyone have an idea what I'm missing in order to get to the answer?

Thanks in advance.

 

[Gene]

Your calculus is fine. Your algebra is failing :evil:
1/2 * 1/(x^(1/2)) * ln(x) =
ln(x)/(2x^(1/2))

(x^(1/2)) * 1/x =
1/x^(1/2) =
2/(2x^(1/2))
Add them up
---------------
Gene

 

[MrGinsu]

Your calculus is fine. Your algebra is failing :evil:
1/2 * 1/(x^(1/2)) * ln(x) =
ln(x)/(2x^(1/2))

(x^(1/2)) * 1/x =
1/x^(1/2) =
2/(2x^(1/2))
Add them up
---------------
Gene

Thanks for your help, Gene. It took me a little while of looking at your answer but then my brain gears finally reengaged. Now I rememeber that sqrt(x) / x = 1 / sqrt(x).

Thanks again,

Clayton

 

[Gene]

Good catch. I thought you could do it!
---------------
Gene