Question

cual es la derivada de 1/xln2

Answer 1

$y=\dfrac{1}{x\mathrm{\,\ell n\,2}}\\ \\ \\ \\ \dfrac{dy}{dx}=\dfrac{d}{dx}\left(\dfrac{1}{x\mathrm{\,\ell n\,2}} \right )$


Colocando as constantes para fora da derivada,

$\dfrac{dy}{dx}=\dfrac{1}{\mathrm{\ell n\,}2}\cdot\dfrac{d}{dx}\left(\dfrac{1}{x} \right )\\ \\ \\ \dfrac{dy}{dx}=\dfrac{1}{\mathrm{\ell n\,}2}\cdot\dfrac{d}{dx}\,(x^{-1})$


A derivada de $x^{n}$ é $n\,x^{n-1}:$

$\dfrac{dy}{dx}=-\dfrac{1}{\mathrm{\ell n\,}2}\cdot x^{-2}\\ \\ \\ \dfrac{dy}{dx}=-\dfrac{1}{\mathrm{\ell n\,}2}\cdot \dfrac{1}{x^{2}}\\ \\ \\ \dfrac{dy}{dx}=-\dfrac{1}{x^{2}\mathrm{\,\ell n\,}2}$