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Math Help - Find Derivative

  1. #1
    Member
    Joined
    Jan 2008
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    118

    Find Derivative

    y = (cot x) / (1 + cot x)


    I got down to
    (sec x tan x) / (1 + cot x) ^2


    I dont know if this is right...
    The correct answer is...
    (-csc^2x) / (1 + cot x)^2

    Can someone help me out? Thanks!
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  2. #2
    Super Member redsoxfan325's Avatar
    Joined
    Feb 2009
    From
    Swampscott, MA
    Posts
    943
    Quote Originally Posted by Morgan82 View Post
    y = (cot x) / (1 + cot x)


    I got down to
    (sec x tan x) / (1 + cot x) ^2


    I dont know if this is right...
    The correct answer is...
    (-csc^2x) / (1 + cot x)^2

    Can someone help me out? Thanks!
    Use the quotient rule: \frac{d}{dx}\left[\frac{f(x)}{g(x)}\right]=\frac{g(x)f'(x)-f(x)g'(x)}{g^2(x)}

    \frac{(1+\cot x)(-\csc^2x)-(\cot x)(-\csc^2x)}{(1+\cot x)^2}=\frac{-\csc^2x(1+\cot x-\cot x)}{(1+\cot x)^2} = \frac{-\csc^2x}{(1+\cot x)^2}
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