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Trig Differentiation

  1. Nov 27, 2011 #1

    jsmith613

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    1. The problem statement, all variables and given/known data

    how is the differential of 1+tan2(4x)

    8*tan(4x)*sec2(4x)

    2. Relevant equations



    3. The attempt at a solution
    So 1 differentiates to 0 (we can now ignore this)
    tan2(4x) differentiates to 2*tan(4x)*sec2(4x)?

    BRING POWER FORWARD, DOWN POWER BY 1, DIFFERENTIATE TERM IN BRACKET
    by the chain rule?
     
    jsmith613, Nov 27, 2011
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  3. Nov 27, 2011 #2

    BloodyFrozen

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    You stated it in your question, but never differentiated the term inside inside the bracket.

    [tex]2 \cdot tan(4x)sec^{2}(4x) \cdot \frac{d}{dx} (4x)~=~[/tex]
     
    Last edited: Nov 27, 2011
    BloodyFrozen, Nov 27, 2011
  4. Nov 27, 2011 #3

    jsmith613

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    hold on
    yours goes to 32....
    NOT 8...
     
    jsmith613, Nov 27, 2011
  5. Nov 27, 2011 #4

    BloodyFrozen

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    My mistake :tongue: I fixed it in my first post ( coefficient was originally wrong), but my point still holds. You ALSO need to differentiate the 4x.
     
    BloodyFrozen, Nov 27, 2011
  6. Nov 27, 2011 #5

    jsmith613

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    oh of course
    differentiate u2 = 2u
    differentiate sec2(4x) is 4*sec(4x)*tan(4x)
    multiply differntials to give
    2*sec(4x)*4*sec(4x)*tan(4x)
     
    jsmith613, Nov 27, 2011
  7. Nov 27, 2011 #6

    BloodyFrozen

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    Exactly!!:approve:
     
    BloodyFrozen, Nov 27, 2011
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