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Homework Help: Is this Correct

  1. Oct 11, 2011 #1
    find the derivatives

    of differentiation of trigonometric functions

    1. y=cos(3x^2+8x-2)

    2. y=tan^3 2x

    3. y=sin5x sin^5 x

    4. y=Square root of 4sin^2x+9cos^2x

    help here please..

    i cant understand trigonometric functions

    sorry admin or moderator, i just search the net on how to do this problems.. and this are my answer

    for
    1. -6x+8sin(3x^2+8x-2)

    2. 6 tan 2x sec^2 2x

    3. 5 cos 5x 5 sin x cos x or 5 cos 5x 5 sin^4 x cos x

    4. 8 sec^4 2x tan 2x

    Are my answers correct.. Help me please
     
  2. jcsd
  3. Oct 11, 2011 #2
    let us do it one by one:
    (1) is not correct.
     
  4. Oct 11, 2011 #3
    (2) is basically correct except that it should be tan^2 since the derivative of tan^3 is 3tan^2...
     
  5. Oct 11, 2011 #4
    re 1.

    1st step: derivative of cos(...)
    2nd step: MULTIPLY by the derivative of (3x^2+8x-2)
     
  6. Oct 11, 2011 #5

    SammyS

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    Actually, (1) is nearly correct.

    Use parentheses around (6x+8), the derivative of 3x^2+8x-2 .

    Start (3) by using the product rule.


    By the Way: Until you get the hang of this, it's probably best to write trig functions raised to a power as:

    (sin(x))5 rather than sin5(x),

    (tan(2x))3 rather than tan3(2x)
     
    Last edited: Oct 11, 2011
  7. Oct 11, 2011 #6
    so my answer in number 1 should be

    -(6x+8)sin(3x^2+8x-2)

    and in number to should be

    6 tan^2 2x sec^2 2x

    Am i correct.. or still wrong :)
     
  8. Oct 11, 2011 #7
    in number 1

    -sin(3x^2+8x-2)(6x+8) then multiply -sin to (6x+8)

    -(6x+8)sin(3x^2+8x-2)

    am i correct now guys :)
     
  9. Oct 11, 2011 #8

    SammyS

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    Either one is OK !
     
  10. Oct 11, 2011 #9
    thanks sammy..

    its now 9 am here we nid to pass this by 10am

    thanks for help...
    but how about my number 3 and number 4

    is that correct? im not sure what i've done..

    especially number 4 with square root thing :)
     
  11. Oct 11, 2011 #10

    SammyS

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    Look at √x as x1/2,

    So y=√(4sin^2x+9cos^2x)

    becomes y=(4sin^2x+9cos^2x)1/2.

    Have fun.
     
  12. Oct 11, 2011 #11

    SammyS

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    For #3. Use the product rule.

    y = {sin5x}×{(sin x)5}
     
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