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Thread: Differentiation + range help needed

  1. #1
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    Differentiation + range help needed

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

    Thanks in advance
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  2. #2
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    Re: Differentiation + range help needed

    Quote Originally Posted by nubshat View Post
    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?
    Thanks from nubshat
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    Re: Differentiation + range help needed

    Yes thank you very much
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    Re: Differentiation + range help needed

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