Question

Determine a derivada:

Answer 1

Boa noite!

$g(x)=\ln\dfrac{e^x+e^{-x}}{2}\\g'(x)=\dfrac{1}{\dfrac{e^x+e^{-x}}{2}}\cdot\left(\dfrac{e^x+e^{-x}}{2}\right)'\\g'(x)=\dfrac{2}{e^x+e^{-x}}\cdot\dfrac{e^x+e^{-x}\cdot\left(-x\right)'}{2}\\g'(x)=\dfrac{2}{e^x+e^{-x}}\cdot\dfrac{e^x-e^{-x}}{2}\\g'(x)=\dfrac{e^{2x}-1}{e^{2x}+1}$

Espero ter ajudado!