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Math Help - Differnetiation

  1. #1
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    Singapore
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    Differnetiation

    Hi I just finished some questions and got these wrong, I won't get to ask anyone till a few days late, so I would really appreciate your help!

    1.) Differentiate \frac{1}{\sin\2\theta}
    Using quotient rule, I got \frac{-2\cos\2\theta}{\sin^2\2\theta}
    Simplifying,
    -2(\cot\2\theta\ cosec\2\theta), why is this wrong?

    2.) Differentiate \tan^3(2x+1)
    I got 6\tan^2\(2x+1)\sec^2\(2x+1), why is this wrong?

    3.) If a, b and c are functions such that a(x) are not 0 for all x and c(x) = a(x)b(x) then c'(d)=0 for d is all real numbers such that a'(d)=0 or b'(d) =0.
    I wrote that it's true becuase I thought the last part of the question made sense..but it's false, why is it so?

    4.) Suppose a,b and c are functions such that a(x) is not 0 for all x and c(x) = b(a(x)) then c'(d)=0 for d is all real numbers such that a'(d)=0.
    I wasn't sure so I thought it was false..

    Thank you!
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  2. #2
    Senior Member
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    Pennsylvania, USA
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    Re: Differnetiation

    Quote Originally Posted by Tutu View Post
    Hi I just finished some questions and got these wrong, I won't get to ask anyone till a few days late, so I would really appreciate your help!
    1.) Differentiate \frac{1}{\sin\2\theta}
    Using quotient rule, I got \frac{-2\cos\2\theta}{\sin^2\2\theta}
    Simplifying,
    -2(\cot\2\theta\ cosec\2\theta), why is this wrong?
    Your answer here is correct. Perhaps your instructor wanted you to further simplify the expression using double-angle formulae? Still, I believe that's overkill. Why do you believe your solution is incorrect?
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  3. #3
    Senior Member
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    Mar 2008
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    Pennsylvania, USA
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    Re: Differnetiation

    Quote Originally Posted by Tutu View Post
    2.) Differentiate \tan^3(2x+1)
    I got 6\tan^2\(2x+1)\sec^2\(2x+1), why is this wrong?
    Again, why do you say you are wrong? Your answer here is correct, as well.
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