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d-dx-x-2-4-




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

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