What is the first derivative of x(t) with a missing factor of w?

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What is the first derivative of

x(t) = Acos(wt) + Bsin(wt) + \frac{F}{2mw}tsin(wt)

I find:

-Awsin(wt) + Bwcos(wt) + \frac{Ftcos(wt)+Fsin(wt)}{2mw}

is correct ?
 
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I believe you're missing a factor of w in the first term of the numerator of the fraction.
 
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