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krypton Group Title

inverse and inverse trignometric functions find d/dx(arctan^2(sqrt(x))

  • 2 years ago
  • 2 years ago

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  1. hsmt Group Title
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    hi krypton.. you still there? I think i might be able to help if you are

    • 2 years ago
  2. krypton Group Title
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    yea dear

    • 2 years ago
  3. hsmt Group Title
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    consider the derivative of arctan^2(u) where u=sqrt x and use the chain rule...

    • 2 years ago
  4. hsmt Group Title
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    sorry. let's start with the derivative of (tan-1u)^2. what is the derivative of this little beastie. lol there we go...

    • 2 years ago
  5. krypton Group Title
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    u mean?

    • 2 years ago
  6. hsmt Group Title
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    what is the derivative of (f(x))^2?

    • 2 years ago
  7. hsmt Group Title
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    it would be something like 2(f(x))times f prime of x

    • 2 years ago
  8. hsmt Group Title
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    in this case, f(u)=tan-1u, where u=sqrt of x. does this make sense?

    • 2 years ago
  9. hsmt Group Title
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    questions are good here. the more you ask, the more i can help... :)

    • 2 years ago
  10. krypton Group Title
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    yea

    • 2 years ago
  11. hsmt Group Title
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    so what is the derivative of tan-1u?

    • 2 years ago
  12. hsmt Group Title
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    you can give me your best guess if you like

    • 2 years ago
  13. krypton Group Title
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    hmm actually i wasnt in the class when the topic was taught, but i thinkis =1/srt 1-x^2?

    • 2 years ago
  14. krypton Group Title
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    sorry 1/1+x^2

    • 2 years ago
  15. hsmt Group Title
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    that is totally correct. :) now replace the x with u so that we can use the chain rule where u=1/sqrtx.

    • 2 years ago
  16. krypton Group Title
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    so thats the answer?

    • 2 years ago
  17. hsmt Group Title
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    no, we have a power of tan-1. so the answer is 2(tan-1(sqrtx))(1/(1+x))1/2sqrtx

    • 2 years ago
  18. hsmt Group Title
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    is that making sense to you?

    • 2 years ago
  19. hsmt Group Title
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    still there?

    • 2 years ago
  20. krypton Group Title
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    ok

    • 2 years ago
  21. krypton Group Title
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    so what will be my final answer?

    • 2 years ago
  22. hsmt Group Title
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    it is above

    • 2 years ago
  23. krypton Group Title
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    can u help me with one other questionÉ

    • 2 years ago
  24. hsmt Group Title
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    if i can, i would be happy to

    • 2 years ago
  25. krypton Group Title
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    find \[find d/dx (\sqrt{1-x ^{2}}+1/2\cos ^{-1}(x) and verify whether or \not this is equal \to (2x+1)d/dx \sin ^{-1}(-x)\]

    • 2 years ago
  26. hsmt Group Title
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    ok. any ideas where to start?

    • 2 years ago
  27. hsmt Group Title
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    oh... and i didnt get anything beyond the arrow... sorry... but i think i have enough to figure it out. :)

    • 2 years ago
  28. krypton Group Title
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    hmm i dont have an idea

    • 2 years ago
  29. hsmt Group Title
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    ok, well, it is a rather large function, but it is a quotient (hint). So where might we start with this lovely little thing?

    • 2 years ago
  30. krypton Group Title
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    hmm..no idea lol

    • 2 years ago
  31. krypton Group Title
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    dont know anytin about the topic yet

    • 2 years ago
  32. hsmt Group Title
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    it is ok... remember the quotient rule d(f/g)/dx=[(fprime)g-(gprime)f]/g^2?

    • 2 years ago
  33. hsmt Group Title
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    in this case the numerator is f=sqrt(1-x^2) +1 and g=2cos-1(x)

    • 2 years ago
  34. hsmt Group Title
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    do you know the product rule?

    • 2 years ago
  35. krypton Group Title
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    yes

    • 2 years ago
  36. hsmt Group Title
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    phew...!! i am so glad. i thought for a sec we were outta options. lol

    • 2 years ago
  37. hsmt Group Title
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    ok

    • 2 years ago
  38. hsmt Group Title
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    look at f(x)=sqrt(1-x^2)+1 and g(x)=(2cos-1(x))^-1. does this make sense?

    • 2 years ago
  39. krypton Group Title
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    hahaha i can still remember my calculus 1, this calculus 2

    • 2 years ago
  40. krypton Group Title
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    yes it does

    • 2 years ago
  41. hsmt Group Title
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    glad to hear it... calc I is totally needed here... good, it makes sense. now we need fprime and gprime and i think you are pretty much homefree. so what is fprime and what is gprime?

    • 2 years ago
  42. hsmt Group Title
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    just algebra after you get the derivatives.

    • 2 years ago
  43. krypton Group Title
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    so i should get the derivative of each of them separatelyÉ

    • 2 years ago
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