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Math Help - Differentiation Help!

  1. #1
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    Differentiation Help!

    Hi,

    f(t) = t Cos w t
    f '(t) =
    f ''(t) =

    Can someone help quick please and tell me how to get the the answers and what rule it is!
    thanks
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  2. #2
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    I think i have worked it out now!
    Product rule?!
    f '(t) = Coswt - wtsinwt
    f ''(t) = ?!?!?!?!
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  3. #3
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    Quote Originally Posted by madcal87 View Post
    I think i have worked it out now!
    Product rule?!
    f '(t) = Coswt - wtsinwt
    f ''(t) = ?!?!?!?!
    Hello,

    1. you used product rule and chain rule - and your result is OK

    2. Use chainrule on the first summand and product rule and chain rule on the second summand. I've got:

    f''(t) = -t \cdot w^2 \cdot \cos(w \cdot t)-2w \cdot \sin(w\cdot t)
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  4. #4
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    for f ' (t) i used the product rule !

    Can u give me a step by step of f '' (t) please.... because im confused!
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  5. #5
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    Quote Originally Posted by madcal87 View Post
    for f ' (t) i used the product rule !

    Can u give me a step by step of f '' (t) please.... because im confused!
    Hi,

    Ok here we go:
    Your result: f '(t) = \cos(wt) - wt\sin(wt)

    <br />
f '(t) = \cos(wt) - wt\sin(wt)=-w(\underbrace{t \cdot  \sin(wt)}_{\text{use product rule}}) + \underbrace{\cos(wt)}_{\text{use chain rule}}

    f''(t)=-w(\sin(wt)+t \cdot (cos(wt) \cdot w)-\sin(wt) \cdot w
    Expand the bracket and collect like terms.
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