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y-sin-1-x-y-




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

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