Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 4th derivative of cos(2x)

  1. Apr 10, 2012 #1
    1. The problem statement, all variables and given/known data

    see title.

    2. Relevant equations
    no


    3. The attempt at a solution

    Ok so the solution is 16cos(2x) but I'm not sure how it is derived to that. I've tried the product rule but it's not working for me. What rule or rules do I use to get this solution?
     
  2. jcsd
  3. Apr 10, 2012 #2
    Well if you calculate the first derivative properly you should be yielded to -2sin(2x).



    Edit: Take into consideration that the derivative of cos(Ux)= -u'(x)*sin(x)
     
  4. Apr 12, 2012 #3
    Ok cool but what rule did you use there?
     
  5. Apr 12, 2012 #4
    The chain rule.
     
  6. Apr 12, 2012 #5

    HallsofIvy

    User Avatar
    Science Advisor

    You don't need the product rule because do not have a product of two functions of x. You need the chain rule because you have f(y)= 2cos(y) and y= 2x:
    [tex]\frac{df}{dx}= \frac{df}{dy}\frac{dy}{dx}[/tex]
    With f(y)= cos(y), what is df/dy? With y= 2x, what is dy/dx?
     
  7. Apr 12, 2012 #6

    Mark44

    Staff: Mentor

    Make that f(y)= cos(y)
     
  8. Apr 12, 2012 #7

    HallsofIvy

    User Avatar
    Science Advisor

    Right. Thanks for the correction.
     
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook