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Math Help - Trigonometric derivatives?

  1. #1
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    Trigonometric derivatives?

    y=5x csc x Did I differentiate this correctly


    5x-cscxcotx+cscx 5 I used the product rule


    My second question is

    y=-cscx-sin(x)
    Last edited by mr fantastic; July 19th 2011 at 02:10 PM.
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    Re: Trigonometric derivatives?

    Quote Originally Posted by homeylova223 View Post
    y=5x csc x Did I differentiate this correctly


    5x-cscxcotx+cscx 5 I used the product rule
    There should only be two terms when you use the product rule - not three. I suspect you mean -5x \csc(x)\cot(x) + 5\csc(x) which is the correct.


    Spoiler:
    My second question is

    y=x^2 sin(x)+2x cos(x) This is what I did


    (x^2)cos(x)+2x -sin(x)+2x sin(x)+2 cos(x) Have I done this correctly
    You need to pay more attention to your signs and how you show them: a \times -b must never be written as a-b but instead -ab


    Spoiler:
    x^2 \cos(x) + 2x\sin(x) - 2x \sin(x) + 2\cos(x) = \cos(x)(x^2+2)


    edit: I put the original second question in a spoiler since the OP edited it out


    For your (new) second equation you can take the derivatives separately. y = -\csc(x) - \sin(x)

    If you don't know the derivative of -csc(x) then you can write it as -(\sin(x))^{-1} and use the chain rule.
    Last edited by e^(i*pi); July 19th 2011 at 11:27 AM. Reason: see post
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    Re: Trigonometric derivatives?

    Ah I have not learned the chain rule yet only the product,quotient, and power rule.

    But this is what I did

    -csc(x)-cos(x)+cot(x)csc(x)-sin(x) I tried using the product rule
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    Re: Trigonometric derivatives?

    Is your question y = -\csc(x) \times - \sin(x) or y = -\csc(x) - \sin(x) -- the latter is subtraction.

    Since you've used the product rule I suspect it's the former. If so use the fact that \sin(x)\csc(x) = 1


    \csc(x)\cos(x)-\cot(x)\csc(x)\sin(x)
    That can be simplified:

    \csc(x)\cos(x) - \cot(x)\csc(x)\sin(x) = \dfrac{\cos(x)}{\sin(x)} - \dfrac{\cos(x)\sin(x)}{\sin(x)\sin(x)} = 0

    -----------------------------------------------

    edit: Please tidy your work up

    -csc(x)-cos(x)+cot(x)csc(x)-sin(x) = -\csc(x)-\cos(x)+\cot(x)\csc(x) - \sin(x) which clearly isn't right.

    If you must use plain text then put it as -csc(x)*-cos(x)+cot(x)csc(x)*-sin(x) so we know you're multiplying by a negative number rather than subtracting.
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