Arcsine Question

Discussion in 'Math' started by ElectronicsFanatic, Apr 9, 2012.

  1. ElectronicsFanatic

    Thread Starter Member

    Feb 12, 2012
    30
    1
    Ok I just got done taking a test and I wasn't sure the answer to the following question. Maybe someone can help me understand this better. This is all new material to me so I am having some trouble getting it down.

    What is wrong with a problem that requires finding the derivative y=arcsin(x²+1)

    I know the formula for this is \frac{1}{\sqrt{1-u^2

    I don't understand why this wont work? Does anyone have any hints to send my way. I really don't know why it wouldn't work
     
  2. DerStrom8

    Well-Known Member

    Feb 20, 2011
    2,428
    1,328
    Well, if you set x^2 + 1 equal to 0 and try to solve for x, you're going to get an imaginary number. You can't take the arcsin of an imaginary number. That is if I'm remembering my factoring correctly :D:p
     
    ElectronicsFanatic likes this.
  3. amilton542

    Active Member

    Nov 13, 2010
    494
    64
    It's a composite function.

    You need to use the chain-rule: dy/dx = [(dy/du)(du/dx)]

    The change in u cancels.
     
    ElectronicsFanatic likes this.
  4. DerStrom8

    Well-Known Member

    Feb 20, 2011
    2,428
    1,328
    Why are you taking the derivative? It's a simple arcsin question (sin^-1). It's to find the angle of a specific value on a coordinate plane. Nothing more.
     
  5. amilton542

    Active Member

    Nov 13, 2010
    494
    64
    If you refer to the question carefully, he said, "What is wrong with a problem that requires finding the derivative y=arcsin(x²+1)."

     
    DerStrom8 likes this.
  6. DerStrom8

    Well-Known Member

    Feb 20, 2011
    2,428
    1,328
    Oh geez. So sorry about that. I misread it :rolleyes:

    My mistake. Please carry on!
     
  7. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    consider

    x² >= 0 thus

    (x²+1) >= 1
    and only equal if x=0.

    But sin (θ) <= 1

    so the only value of x that you can take this arc sin is x=0

    You cannot take the differential of a function that has a single point - it does not vary.
     
    ElectronicsFanatic likes this.
  8. amilton542

    Active Member

    Nov 13, 2010
    494
    64
    I don't believe it. Thanks for pointing that out, I missed that one. I need to observe a function more carefully before approaching it, thanks Studiot!
     
    ElectronicsFanatic likes this.
  9. ElectronicsFanatic

    Thread Starter Member

    Feb 12, 2012
    30
    1
    Ok, I think I get what you guys are all saying, so, I am going to go through this process using the formula I have learned and anyone let me know when I make a mistake.

    \frac{2x}{1}\times\frac{1}{\sqrt{1-(x^2+1)^2}}


    \frac{2x}{\sqrt{1-(x^2+1)^2}

    This is where I start to not quite understand

    I think the final answer would be the following:

    \frac{2}{\sqrt{-1(x^2+1)}}



    When I set x^2+1=0 I understand how I am getting an imaginary number.

    That would be x=\sqrt{-1}

    So what happened to the square on (x^2+1)^2 to just become (x^2+1)

    I am probably making this harder than it needs to be. I really understand what you guys are all saying I am trying to relate it to the formula. Thanks everyone for the answers. I am understanding it a whole lot better than i did before.
     
  10. amilton542

    Active Member

    Nov 13, 2010
    494
    64
    Look at post #7.
     
  11. ElectronicsFanatic

    Thread Starter Member

    Feb 12, 2012
    30
    1
    ok I applied the chain rule to  (x^2+1)^2 as you stated amilton542. I can now see how the answer is applied.

    That took a little longer than i wanted but i understand now thanks everyone. I think Studiot made it the easiest to understand. I am still trying to remember to apply easier methods to the problems. You guys are all a wealth of information. I wont forget that one again.
     
    Last edited: Apr 9, 2012
  12. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    I think you were directed to my post#7.

    y=arcsin(x²+1)

    Has no derivative.

    That is dy/dx does not exist anywhere.

    Oh and welcome to All About Circuits.
     
  13. amilton542

    Active Member

    Nov 13, 2010
    494
    64
    Nooooooo, the functions fixed its not changing thats the problem.

    I would like to apologise for giving you the chain-rule, I read your question to fast.

    Refer to what studiot has pointed-out, its post #7.
     
  14. DerStrom8

    Well-Known Member

    Feb 20, 2011
    2,428
    1,328
    dy/dx is usually implied when someone is told to take the derivative of a function, I think.
     
  15. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    There is no neighbourhoods about the points x=0, y= (4n+1)∏/2, which are the only points on the graph of

    y=arcsin(x²+1)

    The function does not exist for any other value of x.
    It is not a question of imaginary numbers, x is not imaginary.
     
    Last edited: Apr 9, 2012
  16. DerStrom8

    Well-Known Member

    Feb 20, 2011
    2,428
    1,328
    Yeah, that was from when I misunderstood the question. I misread it and thought it was just asking to solve it, not take the derivative.
     
  17. studiot

    AAC Fanatic!

    Nov 9, 2007
    5,005
    513
    So does our new member now understand?
     
  18. ElectronicsFanatic

    Thread Starter Member

    Feb 12, 2012
    30
    1
    Yes. Thanks everyone. The farthest I got in math was precalculus about 12 years ago in high school. This is all new material for me so I appreciate everyone being patient with me and all the help.

    I am slowly trying to remember everything I have learned thus far. I am just about done with Calculus I and will take a break from math for a couple of months and start up again with Calculus II in June. I hope to have all my math finished by December so I can then focus on all the funner parts of electronics. Not that I don't like math, because I enjoy trying to figure things out using math. It just isn't always fun.:D
     
Loading...