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 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.
$\displaystyle \displaystyle\frac{1}{1+\displaystyle\frac{x^2}{4} }\times\frac{1}{2}$
$\displaystyle =\displaystyle\frac{1}{2+\frac{x^2}{2}}$
$\displaystyle =\displaystyle\frac{1}{2+\frac{x^2}{2}}\times 1$
$\displaystyle =\displaystyle\frac{1}{2+\frac{x^2}{2}}\times\frac {2}{2}$
$\displaystyle =\displaystyle\frac{2}{4+x^2}$
I assume the original function is $\displaystyle \displaystyle y = \arctan\left(\frac{x}{2}\right)$
$\displaystyle \displaystyle u = \frac{x}{2}$
$\displaystyle \displaystyle \frac{d}{dx} \arctan(u) = \frac{1}{1+u^2} \cdot \frac{du}{dx}$
the $\displaystyle \displaystyle\frac{1}{2}$ is $\displaystyle \displaystyle \frac{du}{dx}$
$\displaystyle \displaystyle \frac{\frac{1}{2}}{1 + \frac{x^2}{4}} \cdot \frac{4}{4} = \frac{2}{4 + x^2}$