# Thread: Differentiation + range help needed

1. ## Differentiation + range help needed

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

2. ## Re: Differentiation + range help needed

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

$2+e^{\tan(x)} > 2$

The domain of the natural logarithm is positive real numbers.

so the domain must be all real numbers.

$\frac{dy}{dx}=\frac{1}{2+e^{\tan(x)}}\frac{d}{dx }\left( 2+e^{\tan(x) }\right)$

Can you finish from here?

3. ## Re: Differentiation + range help needed

Yes thank you very much

4. ## Re: Differentiation + range help needed

Originally Posted by nubshat
Yes thank you very much
Don't forget that you still must exclude the "bad points" of $\tan(x)$