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Homework Help: Differentiating trigonometric F'ns with double angles

  1. Mar 9, 2013 #1
    1. The problem statement, all variables and given/known data
    With respect to x

    2. Relevant equations

    3. The attempt at a solution

    My question is whether I can simply use d/dx (Tan x) = Sec^2(X) to extrapolate that to d/dx(tan 2x) = Sec^2(2x) ?

    Or do I have to convert to sine/cosine and go from there?
  2. jcsd
  3. Mar 9, 2013 #2


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    Education Advisor


    You I want to point out that (tan2x)' does not equal to sec^2(2x). (Error in technique).

    However, the generally idea isn ok (assuming you using the chain rule in regards to sin(tan(2x)).
  4. Mar 9, 2013 #3
    So this problem can't be solved by using the chain rule thusly:

    d/dx Sin(tan 2x) = cos(tan2x)Sec^2(2x)?

    It turns into:

    Sin(tan 2x) (2)d/dx [sinxcosx / (cos^2(X) - Sin^2(x))]

    quotient rule etc... damn this is gonna be messy. Am I on the right track at least?
    Last edited: Mar 10, 2013
  5. Mar 10, 2013 #4


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    "d/dx Sin(tan 2x) = cos(tan2x)Sec^2(2x)?"

    This is essentially correct, but you're making an error when you take the derivative of tan2x. I'm hoping you look at that part just a little harder and figure out what that error exactly is.
  6. Mar 10, 2013 #5
    d/dx tan 2x = [sec^2 (2x)] (2)

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