y=ln(2 + e^tan(x)). Give the domain of y and find dy/dx
Thanks in advance
The doman of the natural log is
The exponential function is always non negative so this gives
$\displaystyle 2+e^{\tan(x)} > 2$
The domain of the natural logarithm is positive real numbers.
so the domain must be all real numbers.
$\displaystyle \frac{dy}{dx}=\frac{1}{2+e^{\tan(x)}}\frac{d}{dx }\left( 2+e^{\tan(x) }\right)$
Can you finish from here?