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Derivative of Trigonometric Functions

  1. Sep 21, 2013 #1
    1. The problem statement, all variables and given/known data
    d/dx(sec(x)/1+tan(x)
    Evaluate at x=∏/6
    2. Relevant equations



    3. The attempt at a solution
    ((1/cos(x))(1+tan(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))^2

    ((1/cos(x))-(sec(x))(sin(x)/cos(x)))/(1+tan(x))

    I used the quotient rule and reduced what I could. Have I done this right and can I go any further before evaluating? Thank you.
     
  2. jcsd
  3. Sep 21, 2013 #2

    vela

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    No, that's not correct. Applying the quotient rule involves taking some derivatives. It doesn't appear you've done that.
     
  4. Sep 21, 2013 #3
    Of course I have. 1/cos(x) is the derivative of sec(x) and (sin(x)/cos(x)) is the derivative of (1+tan(x)) are they not?
     
  5. Sep 21, 2013 #4

    vela

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    No, they're not.
     
  6. Sep 21, 2013 #5
    Right, they are not. Hahaha. Don't mind my red cheeks.
     
  7. Sep 21, 2013 #6
    =((1+tanx)(secxtanx)-(secx)(sec^2x))/(1+tanx)2
    =(secxtanx+secxtan^2x-sec^3x)/(1+tanx)2

    Is this looking any closer to a correct answer?
     
  8. Sep 21, 2013 #7

    arildno

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  9. Sep 22, 2013 #8
    Is this as far as it goes? Can it be simplified any more?
     
  10. Sep 22, 2013 #9

    Mark44

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    I realize that you already recognized that these are wrong, but I thought it worth mentioning why they were wrong.

    sec(x) = 1/cos(x) - This is an identity and is how the secant function is defined. It has nothing to do with derivatives.

    tan(x) = sin(x)/cos(x) - This is also an identity and is how the tangent function is defined. This is unrelated to derivatives.
     
  11. Sep 22, 2013 #10
    Yes, I was simply confusing myself. As far as my current work, can it be simplified any more?
     
  12. Sep 22, 2013 #11

    Mark44

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    You might be able to, but what's the point? Just go ahead and evaluate it now at x = ##\pi/6##.
     
  13. Sep 22, 2013 #12
    ((2/√3)(√3/3)+((2/√3)(1/3))-(8/3^(3/2)))/(4/3)+((2√3)/3)
    =(2/9+2/(3√3)-8/(3^3/2))/((2(2√3+1))/3√3)
     
  14. Sep 22, 2013 #13
    Can anyone tell me if I am on the right track please?
     
  15. Sep 22, 2013 #14

    Mark44

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    The above is fine, but what you have below is difficult to read, especially what you have on the right side of the =. Please simplify it.


     
  16. Sep 22, 2013 #15
    Let's try this
     

    Attached Files:

  17. Sep 22, 2013 #16
    Oh I guess I could change the term in the denominator to 4/3.
     
  18. Sep 23, 2013 #17
  19. Sep 23, 2013 #18

    Mark44

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    In the 3rd line of your attachment, the sign of the last term mysteriously changed.
     
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