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Differentiation Problem

  1. May 11, 2010 #1
    Find the derivative of the following:
    y = 1/ COS(t^2)

    2. Relevant equations

    Here is my attempt

    Using (Cos(t^2))^-1

    SOlve using the chain rule:

    u = t^2
    du = 2t
    dy/dt = -1.(-sin(u))^(-2) .(2t)
    = -2t(-sin(u))^(-2)

    = -2t/(Sin(t^2))^2

    Is this correct or have I totally used the wrong techiniques?
  2. jcsd
  3. May 11, 2010 #2


    User Avatar
    Science Advisor

    This isn't correct. Try applying the chain rule twice, starting with u=cos(t^2).
  4. May 11, 2010 #3
    You can do it whatever way you want, but I would use the quotient rule. It seems less confusing to me.
  5. May 11, 2010 #4


    Staff: Mentor

    Your function is the same as sec(t^2). If you know the rule for the derivative of the secant function, you can use that (plus the chain rule).
  6. May 11, 2010 #5
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