y=ln(2 + e^tan(x)). Give the domain of y and find dy/dx

Thanks in advance:)

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- Oct 6th 2012, 08:55 AMnubshatDifferentiation + range help needed
y=ln(2 + e^tan(x)). Give the domain of y and find dy/dx

Thanks in advance:) - Oct 6th 2012, 09:02 AMTheEmptySetRe: Differentiation + range help needed
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? - Oct 6th 2012, 09:08 AMnubshatRe: Differentiation + range help needed
Yes thank you very much

- Oct 6th 2012, 09:44 AMTheEmptySetRe: Differentiation + range help needed