# Differentiation + range help needed

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

• Oct 6th 2012, 09:02 AM
TheEmptySet
Re: Differentiation + range help needed
Quote:

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

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 AM
nubshat
Re: Differentiation + range help needed
Yes thank you very much
• Oct 6th 2012, 09:44 AM
TheEmptySet
Re: Differentiation + range help needed
Quote:

Originally Posted by nubshat
Yes thank you very much

Don't forget that you still must exclude the "bad points" of $\displaystyle \tan(x)$