Question Number 185191 by Shrinava last updated on 18/Jan/23
$$\mathrm{y}\:=\:\mathrm{sin}\:\frac{\mathrm{1}}{\mathrm{x}}\:\:\Rightarrow\:\:\mathrm{y}^{'} \:=\:? \\ $$
Answered by Frix last updated on 18/Jan/23
$${y}={f}\left({g}\left({x}\right)\right)\:\Rightarrow\:{y}'={g}'\left({x}\right)×{f}'\left({g}\left({x}\right)\right) \\ $$$${y}=\mathrm{sin}\:\frac{\mathrm{1}}{{x}}\:\Rightarrow\:{y}'=−\frac{\mathrm{1}}{{x}^{\mathrm{2}} }\mathrm{cos}\:\frac{\mathrm{1}}{{x}} \\ $$