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Differentiation (Trig Function)

  1. Oct 9, 2008 #1
    2. Relevant equations

    Take the second derivative of:
    cos(x^2)

    3. The attempt at a solution

    cos(x^2)

    dy/du = -sin(u)
    du/dx = 2x

    dy/dx= -2xsin(x^2)

    I don't know how to begin taking the derivative of this a second time...
     
  2. jcsd
  3. Oct 9, 2008 #2

    danago

    User Avatar
    Gold Member

    What rule do you think you will need to use?
     
  4. Oct 9, 2008 #3
    Use the product rule with -2x and sin(x^2). You'll have to use the chain rule again when you calculate the derivative of sin(x^2).
     
  5. Oct 9, 2008 #4
    So I'd have 2xcos(u) + -2sin(u)

    How am I to use the chain rule at this point?

    Ugh I don't understand how combine rules with composite functions.
     
  6. Oct 9, 2008 #5
    nm...

    Solution should be as follows:
    -2xsin(x^2)

    dy/du= sin(u)
    du/dx= 2x

    -2xsin(u) + -2xsin(U)

    -2xcos(u) + -2sin(u)

    = 2x(-2xcos(x^2) + -2sin(x^2))

    Could someone please confirm? Thank you for the help.
     
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