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Homework Help: Simplifying a derivative

  1. Oct 11, 2008 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of
    [tex]f(x)=2x^3+cos^2(x^3)[/tex]

    3. The attempt at a solution

    [tex]f'(x)=6x^2+2cos(x^3)*-sin(x^3)*3x^2[/tex]
    [tex]f'(x)=6x^2-6x^2cos(x^3)sin(x^3)[/tex]

    The book has a different solution since they always simplify, but how would I simplify it? I know it has something to do with the 6x2, but the 2nd 6x2 is attached to the cos.
     
  2. jcsd
  3. Oct 11, 2008 #2

    Defennder

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    Just use the double angle formula for sin. What is sin2x for example?
     
  4. Oct 11, 2008 #3
    Never heard of it :confused:
     
  5. Oct 11, 2008 #4

    gabbagabbahey

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    It's a Trig Identity that you should have come across in high school:

    [tex]sin(2\theta)=2sin(\theta)cos(\theta)[/tex]
     
  6. Oct 11, 2008 #5
    I'm still in high school...
     
  7. Oct 11, 2008 #6

    HallsofIvy

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    Okay, so factor it out:
    [tex]f'(x)= 6x^2(1- cos(x^3)sin(x^3))[/tex]
    You don't say WHAT the "different solution" in the book is so I don't know if you want that simplified more. You could use the identity Defennder gave you: Since sin(2x3)= 2sin(x3)cos(x3, cos(x3)sin(x3= (1/2)sin(2x3).

    Whether you are in High School or not, taking a course before learning the pre-requisites for that course is just wasting your time. And trigonometry is definitely a pre-requisite for problems like this.
     
  8. Oct 11, 2008 #7
    I've taken PreCalc. I just don't recall learning that identity. Maybe I just forgot or it was called by a different name. The only identities that I really remember well is the basic Pythagorean identity.

    Thanks for the help though.
     
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