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Math Help - differentiating trig function xsinx+cosx

  1. #1
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    differentiating trig function xsinx+cosx

    Hi there, I'm having a conflict with the book I'm using.
    The question is asking to differentiate

    {x}sin{x}+cos{x}

    I use the chain rule for the first term and the sum rule for the whole expression to get

    sinxcosx-sinx

    my book however states the answer is

    sinx-xcosx-sinx=xcosx

    What am I doing wrong?
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  2. #2
    Senior Member Sambit's Avatar
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    Quote Originally Posted by flashylightsmeow View Post

    I use the chain rule for the first term and the sum rule for the whole expression to get

    sinxcosx-sinx
    First tell me how did you get this? Explain a bit.
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  3. #3
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    ok, so i treated xsinx as a composite function s(r(x)) where s(x)=....wait a minute...ffs I have to use the product rule don't I? so I get xcosx+sinx-sinx=xcosx!! Thank you!
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  4. #4
    Senior Member Sambit's Avatar
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    Now you got it right. Silly mistake is a very bad habit; try to get rid of it....
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  5. #5
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    Ugh, I know, I have a maths exam coming up and I keep making these stupid mistakes. How do you get rid of them though? Practise?
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  6. #6
    Senior Member Sambit's Avatar
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    Yes. And also concentration. You don't need solve numerous problems each day. Just make sure one thing: whatever you do, you do it correctly.
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  7. #7
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    Thanks Sambit. Will try and apply myself more!
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