Question

A primeira derivada da função y = logax2 é

Answer 1

$\large\boxed{\begin{array}{l}\underline{\rm Derivada\,de\,func_{\!\!,}\tilde oes\,logar\acute itmicas}\\\rm 1)~base~\underline{\bf e}:~\dfrac{d}{dx}[\ln u]=\dfrac{1}{u}\cdot\dfrac{du}{dx}\\\\\rm 2)~base~qualquer:\dfrac{d}{dx}[\log_au]=\dfrac{1}{u\ln a}\cdot\dfrac{du}{dx}\end{array}}$

$\large\boxed{\begin{array}{l}\rm y=\log_ax^2\\\\\rm\dfrac{dy}{dx}=\dfrac{1}{\diagup\!\!\!\!\!x^2\ln a}\cdot2\diagup\!\!\!\!x\\\\\rm\dfrac{dy}{dx}=\dfrac{2}{x\ln a}\end{array}}$