# I can't figure this operation.

• Jan 16th 2011, 08:58 AM
melvis
I can't figure this operation.
I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.
http://img20.imageshack.us/img20/9264/29921333.jpg
I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.
• Jan 16th 2011, 09:18 AM
Quacky
$\displaystyle\frac{1}{1+\displaystyle\frac{x^2}{4} }\times\frac{1}{2}$

$=\displaystyle\frac{1}{2+\frac{x^2}{2}}$

$=\displaystyle\frac{1}{2+\frac{x^2}{2}}\times 1$

$=\displaystyle\frac{1}{2+\frac{x^2}{2}}\times\frac {2}{2}$

$=\displaystyle\frac{2}{4+x^2}$
• Jan 16th 2011, 09:23 AM
skeeter
Quote:

Originally Posted by melvis
I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.
http://img20.imageshack.us/img20/9264/29921333.jpg
I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.

I assume the original function is $\displaystyle y = \arctan\left(\frac{x}{2}\right)$

$\displaystyle u = \frac{x}{2}$

$\displaystyle \frac{d}{dx} \arctan(u) = \frac{1}{1+u^2} \cdot \frac{du}{dx}$

the $\displaystyle\frac{1}{2}$ is $\displaystyle \frac{du}{dx}$

$\displaystyle \frac{\frac{1}{2}}{1 + \frac{x^2}{4}} \cdot \frac{4}{4} = \frac{2}{4 + x^2}$
• Jan 16th 2011, 09:23 AM
melvis
thx mate :D
• Jan 16th 2011, 09:30 AM
ahaok
Quote:

Originally Posted by melvis
I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.
http://img20.imageshack.us/img20/9264/29921333.jpg
I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.

http://screencast.com/t/n2gG1KqR
• Jan 16th 2011, 01:33 PM
HallsofIvy
Quote:

Originally Posted by melvis
I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.
http://img20.imageshack.us/img20/9264/29921333.jpg
I'm not sure how that 2 got on the denominator, if somebody can tell me the steps they used, I would appreciate that. Thx for the help.

In order to get rid of the "4" in $\frac{x^2}{4}$ multiply both numerator and denominator by "4".
$\frac{4}{4\left(1+ \frac{x^2}{4}\right)}\frac{1}{2}= \frac{4\left(\frac{1}{2}\right)}{4+ x^2}= \frac{2}{4+ x^2}$