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Inverse Trig Function: Find Derivative of the Function

  1. Jan 19, 2012 #1
    1. The problem statement, all variables and given/known data
    find the derivative of the function
    f(x)=arcsec(4x)


    2. Relevant equations
    I think this is a Relevant equations.

    d/dx[arcsecu]=u'/(|u|(√u2-1)


    3. The attempt at a solution
    f'(x)=4/(|4|(√42-1)
    =1/√15

    I keep getting wrong in my online homework why? :confused:
     
  2. jcsd
  3. Jan 19, 2012 #2

    Dick

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    What happened to the x??
     
  4. Jan 20, 2012 #3
    is it 4/(|4x|(√4x2-1))

    I keep getting it wrong
     
  5. Jan 20, 2012 #4

    HallsofIvy

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    What is u in your original integral? What is [itex]u^2[/itex]?
     
  6. Jan 20, 2012 #5

    Dick

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    That's sort of close. But look up the formula again. Isn't the square root part [itex]\sqrt(u^2-1)[/itex] instead of what you have? And when you write something like 4x^2 it's not clear whether you mean (4x)^2 or 4*(x^2). Which do you mean?
     
  7. Jan 20, 2012 #6
    I mean this one (4x)^2
     
  8. Jan 20, 2012 #7

    Dick

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    Ok, then keep writing it like that. And what about my other question?
     
  9. Jan 20, 2012 #8
    okay how about this answer??

    f'(x)=arcsec4x+ 4/(4x(√(16x)2-1)
     
  10. Jan 20, 2012 #9
    I did this one in my homework online and it keeps saying I'm wrong
     

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  11. Jan 20, 2012 #10

    Dick

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    Stop changing things without giving any reason. Why did you put the arcsec4x in there? Why did you drop the absolute value on |4x|? (4x)^2 was right, (16x)^2 isn't. Why not?
     
  12. Jan 20, 2012 #11

    Dick

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    That looks right, except you have x instead of |x|.
     
  13. Jan 20, 2012 #12
    YAY it finally worked thank you :D
     
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