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Math Help - Simplifying a denominator before taking derivative

  1. #1
    Junior Member beebe's Avatar
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    Simplifying a denominator before taking derivative

    This might be more of a trig question, so if it is would someone kindly move it for me?

    So I'm finding the second derivative of ln[sec(x)+tan(x)]. My first derivative is \frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}.

    My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.
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  2. #2
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    Re: Simplifying a denominator before taking derivative

    Have you considered factoring out sec(x) from the numerator?
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  3. #3
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    Re: Simplifying a denominator before taking derivative

    Quote Originally Posted by beebe View Post
    This might be more of a trig question, so if it is would someone kindly move it for me?

    So I'm finding the second derivative of ln[sec(x)+tan(x)]. My first derivative is \frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}.

    My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.
    Or you could multiply top and bottom by \displaystyle \sec{x} - \tan{x}, since you should know that \displaystyle \sec^2{x} - \tan^2{x} \equiv 1...
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  4. #4
    Junior Member beebe's Avatar
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    Re: Simplifying a denominator before taking derivative

    Thanks guys.

    Quote Originally Posted by TKHunny View Post
    Have you considered factoring out sec(x) from the numerator?
    I feel kinda dumb for missing this one.
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  5. #5
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    Re: Simplifying a denominator before taking derivative

    Quote Originally Posted by beebe View Post
    This might be more of a trig question, so if it is would someone kindly move it for me?

    So I'm finding the second derivative of ln[sec(x)+tan(x)]. My first derivative is \frac{sec(x)tan(x)+sec^2(x)}{sec(x)+tan(x)}.

    My question is: can I simplify this fraction to make taking the second derivative less tedious? I'm capable of doing it without simplifying first, but I don't want to get a super long and ugly answer.
    yes.
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