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Math Help - Trig Derivitive Question

  1. #1
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    Trig Derivitive Question

    This is part of an indeterminate form question in my textbook.

    lim(x -> 0) ((1/x) - (1/sin x)) = lim (x->0) (sinx - x)/(x sinx) = lim (x->0) (cosx -1) / (sinx + x cosx).

    How did the derivitve of (x sinx) become (sinx + x cosx)? Am I forgetting an identitiy that is applied here?
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  2. #2
    MHF Contributor harish21's Avatar
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    The product rule is used to find the derivative of x \; sin(x)

    Look at this and figure out how you differentiate that identity.
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  3. #3
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    Product rule (u x v)' = (u' x v) + (u x v')
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  4. #4
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    Quote Originally Posted by tintin2006 View Post
    Product rule (u x v)' = (u' x v) + (u x v')
    Man I feel so silly now since the reason was so obvious. Thanks.
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