Question

Cálculo I Derivação
Log √x+1
³

Answer 1

Sejam:

• $y=\log_3 u$

• $u=\sqrt{v}$

• $v=x+1$

$\frac{dy}{dx}=\frac{dy}{du}.\frac{du}{dv}.\frac{dv}{dx}\\\\\frac{dy}{dx}=\frac{d}{du}(\log_3 u).\frac{d}{dv}(\sqrt{v}).\frac{d}{dx}(x+1)\\\\\frac{dy}{dx}=\frac{1}{\ln3.u}.\frac{1}{2\sqrt{v}}.1\\\\\frac{dy}{dx}=\frac{1}{2\ln3(\sqrt{x+1})(\sqrt{x+1)}}\\\\\frac{dy}{dx}=\frac{1}{2\ln3(x+1)}$