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Differentiate-y-e-x-2-




Question Number 161209 by CM last updated on 14/Dec/21
Differentiate y=e^(−x^2 )
$${Differentiate}\:{y}={e}^{−{x}^{\mathrm{2}} } \\ $$
Commented by cortano last updated on 14/Dec/21
 ⇔ln y=−x^2   ⇔((y′)/y) = −2x   ⇔ y′ = −2x e^(−x^2 )   ⇔(dy/dx)=−2x e^(−x^2 )
$$\:\Leftrightarrow\mathrm{ln}\:{y}=−{x}^{\mathrm{2}} \\ $$$$\Leftrightarrow\frac{{y}'}{{y}}\:=\:−\mathrm{2}{x}\: \\ $$$$\Leftrightarrow\:{y}'\:=\:−\mathrm{2}{x}\:{e}^{−{x}^{\mathrm{2}} } \\ $$$$\Leftrightarrow\frac{{dy}}{{dx}}=−\mathrm{2}{x}\:{e}^{−{x}^{\mathrm{2}} } \\ $$

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