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Math Help - quotient rule

  1. #1
    Junior Member
    Joined
    Sep 2008
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    71

    quotient rule

    Verify d/dx tan(x) = sec^2 (x) and d/dx cot (x) = -csc^2 (x)
    use the quotient rule.

    so for d/dx tan(x) = sec^2 (x) would it be

    sin(x)/cos(x)=(sec(x)tan(x))^2

    the answer is: sin(x)/cos(x)/(sec(x)tan(x))^2= sec^2 (x) (sin(x)/cos(x))- tan(x)*(sec(x)tan(x))^2/(sec^2)^2


    and for d/dx cot (x) = -csc^2 (x)
    the aswer is
    tan(x)/(csc(x)cot(x)^2= -csc^2(x)(tan(x))-(cot(x))((csc(x))cot(x))^2/-csc^2(x)


    I am really confused please help. I do not kno how 2 reduce or if this is even right can someone please explain the right answer to me thank you
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  2. #2
    Newbie
    Joined
    Oct 2009
    Posts
    11
    the derivative of sin/cos is..
    (cos(x)cos(x)-(sin(x)(-sin(x)))/(cos(x))^2
    then you can simplify it to..
    (cos(x)^2+sin(x)^2)/(cos(x))^2
    now cos(x)^2+sin(x)^2=1 and 1/cos(x)^2 is the same as sec(x)^2
    make sense?
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