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Author: Tinku Tara

find-d-dx-y-where-y-x-x-

Question Number 11552 by Nayon last updated on 28/Mar/17 $${find}\:\frac{{d}}{{dx}}\left({y}\right)\:{where}\:\:{y}=\overset{\sqrt{{x}}} {\:}\sqrt{\sqrt{{x}}} \\ $$$$ \\ $$ Answered by ajfour last updated on 28/Mar/17 $${y}\:=\:\left(\sqrt{{x}}\right)^{\frac{\mathrm{1}}{\:\sqrt{{x}}}} \\ $$$$\mathrm{ln}\:{y}\:=\frac{\mathrm{ln}\:\sqrt{{x}}}{\:\sqrt{{x}}}…

find-d-dx-2-x-

Question Number 11548 by Nayon last updated on 28/Mar/17 $$ \\ $$$${find}\:\frac{{d}}{{dx}}\left(\mathrm{2}^{{x}} \right) \\ $$ Answered by sma3l2996 last updated on 28/Mar/17 $$=\frac{{d}\left({e}^{{xln}\left(\mathrm{2}\right)} \right)}{{dx}}={ln}\left(\mathrm{2}\right){e}^{{xln}\left(\mathrm{2}\right)} ={ln}\left(\mathrm{2}\right)\mathrm{2}^{{x}}…