1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

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!
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook