Question Number 11151 by suci last updated on 14/Mar/17
$${f}\left({x}\right)=\mathrm{2}^{\frac{\mathrm{1}−{x}}{\mathrm{2}+{x}^{\mathrm{2}} }} \\ $$$${f}'\left({x}\right)=…??? \\ $$
Answered by ajfour last updated on 14/Mar/17
![= 2^((1−x)/(2+x^2 )) (ln 2)[((x^2 −2x−2)/((x^2 +2)^2 ))]](https://www.tinkutara.com/question/Q11157.png)
$$=\:\mathrm{2}^{\frac{\mathrm{1}−{x}}{\mathrm{2}+{x}^{\mathrm{2}} }} \left(\mathrm{ln}\:\mathrm{2}\right)\left[\frac{{x}^{\mathrm{2}} −\mathrm{2}{x}−\mathrm{2}}{\left({x}^{\mathrm{2}} +\mathrm{2}\right)^{\mathrm{2}} }\right] \\ $$