I can't figure this operation.

**melvis** · January 16th 2011, 07:58 AM

I can't figure this operation. here is the question with the answer, I just can't figure, how to get there.

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.

**Quacky** · January 16th 2011, 08:18 AM

$\displaystyle\frac{1}{1+\displaystyle\frac{x^2}{4} }\times\frac{1}{2}$

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

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

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

$=\displaystyle\frac{2}{4+x^2}$

**skeeter** · January 16th 2011, 08:23 AM

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.

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 $\displaystyle \frac{du}{dx}$

$\displaystyle \frac{\frac{1}{2}}{1 + \frac{x^2}{4}} \cdot \frac{4}{4} = \frac{2}{4 + x^2}$

**melvis** · January 16th 2011, 08:23 AM

thx mate

**ahaok** · January 16th 2011, 08:30 AM

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.

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

**HallsofIvy** · January 16th 2011, 12:33 PM

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.

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".
$\frac{4}{4\left(1+ \frac{x^2}{4}\right)}\frac{1}{2}= \frac{4\left(\frac{1}{2}\right)}{4+ x^2}= \frac{2}{4+ x^2}$

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