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Homework Help: Product Rule of x = r cos()

  1. Mar 31, 2010 #1
    1. The problem statement, all variables and given/known data

    r = r(t)
    [tex]\theta[/tex] = [tex]\theta[/tex](t)

    x = r cos([tex]\theta[/tex])

    dx/dt =dr/dt cos([tex]\theta[/tex]) - r sin([tex]\theta[/tex]) d[tex]\theta[/tex]/dt

    3. The attempt at a solution

    Where does the d[tex]\theta[/tex]/dt come from at the end of the derivative? I know I'm using product rule here because r and theta are both functions of t. But, the derivative of cos is just -sin. Why would there be a d[tex]\theta[/tex]/dt at the end?
  2. jcsd
  3. Mar 31, 2010 #2


    User Avatar
    Homework Helper
    Gold Member

    No, [itex]\frac{d}{d\theta}\cos\theta=-\sin\theta[/itex] but [itex]\frac{d}{dt}\cos\theta=\left(\frac{d}{d\theta}\cos\theta\right)\left(\frac{d\theta}{dt}\right)[/itex] via the chain rule. :wink:
  4. Mar 31, 2010 #3


    Staff: Mentor

    Chain rule.
    d/dt(cos(theta)) = -sin(theta)*d(theta)/dt
  5. Mar 31, 2010 #4
    oooooooooooooohhhhhhhhhhhh! man I'm kinda disappointed I didn't see that one : ( oh well. Thank very much guys!
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