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Math Help - Find a Derivative

  1. #1
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    Find a Derivative

    Always derivatives...

    Find the derivative of :

    g (x) = arctan {1n [sec √X]}

    I'm confuse when I try to resolve the equation
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  2. #2
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    There's a whole lot of chain rule going on. Let's see what you get.
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  3. #3
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    I get derivative step by step, beginning by :

    Tan
    ª = 1/ (sec²(v))
    {Here I use, v = (sec
    x) and a = -1}

    Then,

    Ln'(v) = 1/v ·
    v'

    Next, internal derivative of v :

    (sec√
    x · Tan√x) · ½ · x
    {I use n = - ½ }


    So, my entire equation would be :

    g(x)' = 1/ (sec²(v) · v'/v · (sec x · Tanx)/2 · xⁿ)
    {I use a = -
    ½}

    Then,

    g'(x)' = √x / (sec²(Ln [sec√x]) · sec√x · Tan√x)

    But I doubt that is correct and I don't know if is possible more simplification

    (I'm sorry for the traslation the terms)
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  4. #4
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    This:

    g (x) = arctan {1n [sec √X]}
    What is that? Is it tan^{-1}(ln[sec\sqrt{x}]) or tan^{-1}\left(\frac{1}{sec\sqrt{x}}\right)
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  5. #5
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    It's true, I'm mistaken...
    It's the first equation that you writed (with a logarithm)

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  6. #6
    MHF Contributor harish21's Avatar
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    Quote Originally Posted by AlanaSan View Post
    It's true, I'm mistaken...
    It's the first equation that you writed (with a logarithm)

    -the derivative of arctan(x) is \frac{1}{1+x^2} ,

    in this case: \frac{1}{log^{2}(\sec(\sqrt{x})+1)}...(1)

    -the derivative of ln(x) is \frac{1}{x} ,

    in this case: \frac{1}{\sec(\sqrt(x))}....(2)

    -the derivative of sec(x) is \sec(x).\tan(x),

    in this case \sec(\sqrt{x}).\tan(\sqrt{x})...(3)

    -finally the sqrt of \sqrt{x} = \frac{1}{2 \sqrt(x)}...(4)

    multiply 1,2,3,and 4 and simplify
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  7. #7
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    Quote Originally Posted by AlanaSan View Post
    It's true, I'm mistaken...
    It's the first equation that you writed (with a logarithm)

    Lets take a look at the derivatives of each of the parts on their own:

    \frac{d(tan^{-1}(x))}{dx}=\frac{1}{1+x^{2}}

    \frac{d(ln(x))}{dx}=\frac{1}{x}

    \frac{d(\sec(x))}{dx}=\sec (x) \tan (x)

    \frac{d(\sqrt{x})}{dx}=\frac{1}{2\sqrt{x}}

    See if you can use the above to make a composition of functions of derivatives - or just use the derivatives to navigate to an answer.
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