Question Number 226878 by Spillover last updated on 17/Dec/25
Answered by gregori last updated on 18/Dec/25
$$\:=\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{\sqrt{{x}}−\sqrt{{x}+{h}}}{\left(\sqrt{{x}+{h}}\:.\sqrt{{x}}\:\right){h}} \\ $$$$\:=\:\frac{\mathrm{1}}{{x}}\:\underset{{h}\rightarrow\mathrm{0}} {\mathrm{lim}}\:\frac{−{h}}{\left(\sqrt{{x}}+\sqrt{{x}+{h}}\:\right){h}} \\ $$$$\:=\:−\frac{\mathrm{1}}{{x}.\:\mathrm{2}\sqrt{{x}}}\:=\:−\frac{\mathrm{1}}{\mathrm{2}{x}\sqrt{{x}}} \\ $$