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Math Help - derivative of arctan

  1. #1
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    derivative of arctan

    hey everyone just doing some calc for fun again :P and i ran across another question i wasnt sure how to do any help would be greatly appreciated

    find the derivative of

    \arctan(\sqrt{1+x}/\sqrt{1-x})<br />
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by IrrationalPI3 View Post
    hey everyone just doing some calc for fun again :P and i ran across another question i wasnt sure how to do any help would be greatly appreciated

    find the derivative of

    \arctan(\sqrt{1+x}/\sqrt{1-x})<br />

    Recall that

    \frac{d}{dx}\left[\arctan{u}\right]=\frac{u'}{1+u^2}

    You have u=\frac{\sqrt{1+x}}{\sqrt{1-x}}

    So plug-n-play.
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  3. #3
    Senior Member DeMath's Avatar
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    Quote Originally Posted by IrrationalPI3 View Post
    hey everyone just doing some calc for fun again :P and i ran across another question i wasnt sure how to do any help would be greatly appreciated

    find the derivative of

    \arctan(\sqrt{1+x}/\sqrt{1-x})<br />
    \arctan \sqrt {\frac{{1 + x}}{{1 - x}}}.

    \frac{d}<br />
{{dx}}\arctan \sqrt {\frac{{1 + x}}<br />
{{1 - x}}}  = {\left[ {1 + {{\left( {\sqrt {\frac{{1 + x}}<br />
{{1 - x}}} } \right)}^2}} \right]^{ - 1}} \cdot \frac{d}<br />
{{dx}}\sqrt {\frac{{1 + x}}<br />
{{1 - x}}}  =

    = \frac{1}<br />
{2}{\left( {1 + \frac{{1 + x}}<br />
{{1 - x}}} \right)^{ - 1}} \cdot \left[ {{{\left( {\frac{{1 + x}}<br />
{{1 - x}}} \right)}^{ - 1/2}} \cdot \frac{d}<br />
{{dx}}\left( {\frac{{1 + x}}<br />
{{1 - x}}} \right)} \right] =

    = \frac{{1 - x}}<br />
{4} \cdot \frac{{\sqrt {1 - x} }}<br />
{{\sqrt {1 + x} }} \cdot \frac{2}<br />
{{{{\left( {1 - x} \right)}^2}}} =  \ldots
    Now simplify

    Your answer must be \frac{1}{{2\sqrt {1 - {x^2}} }}.
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  4. #4
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    wow that was fast thanks people, i will try the method offered and check my answer against the one given. Thanks again

    I guess high school is gonna be boring now that i can do this stuff already lol
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  5. #5
    No one in Particular VonNemo19's Avatar
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    With your attitude, you're gonna go places.

    Stick around here at MHF, we need people like you.
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