Question Number 7665 by upendrakishor99@gmail.com last updated on 08/Sep/16
$$\frac{{d}}{{dx}}\sqrt{{x}^{\mathrm{2}} −\mathrm{4}} \\ $$
Answered by Rasheed Soomro last updated on 08/Sep/16
$$\frac{{d}}{{dx}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{1}/\mathrm{2}} =\frac{\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\left(\mathrm{1}/\mathrm{2}\right)−\mathrm{1}} \frac{{d}}{{dx}}\left({x}^{\mathrm{2}} −\mathrm{4}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{\mathrm{1}}{\mathrm{2}}\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{−\mathrm{1}/\mathrm{2}} \left(\mathrm{2}{x}\right) \\ $$$$\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:\:=\frac{{x}}{\left({x}^{\mathrm{2}} −\mathrm{4}\right)^{\mathrm{1}/\mathrm{2}} }=\frac{{x}}{\sqrt{{x}^{\mathrm{2}} −\mathrm{4}}} \\ $$