1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Find the derivative of function with respect to x

  1. Mar 9, 2013 #1
    Find the derivative of function with respect to x

    y = sin^-1 (x-1/x+1)

    Steps I took:
    = sin(x-1/x+1)^-1
    u = sin(x-1/x+1)
    u' = cos u * u'
    u = x-1/x+1
    u' = t'b - tb'/b^2

    t = x-1
    b = x+1
    t' = 1
    b' = 1
    b^2 = (x+1)(x+1) = x^2+2x+1
    u' = (1)(x+1) - (x-1)(1)/x^2+2x+1
    u' = x+1-x-1 / x^2+2x+1
    u' = 0 !!!

    how can it be zero? something has gone wrong here.

    The answer to the question of 1/(x^(1/2) (x+1))

    Thank you
  2. jcsd
  3. Mar 9, 2013 #2


    User Avatar
    2017 Award

    Staff: Mentor

    There are missing brackets: x-1/x+1 is ##x-\frac{1}{x}+1##. I think you mean (x-1)/(x+1), or ##\frac{x-1}{x+1}##.
    (I added brackets here)
    This step is wrong, check the signs in the numerator.
  4. Mar 9, 2013 #3


    User Avatar
    Staff Emeritus
    Science Advisor
    Homework Helper

    Is the initial function sin or arcsin?

    If it is arcsin, I don't think you have the correct derivative.
  5. Mar 9, 2013 #4
    how would you tell the difference? (sin/arcsin)
  6. Mar 10, 2013 #5


    User Avatar
    Homework Helper

    sin-1 x is the same as arcsin x. I'm assuming that your original function is
    [itex]y = sin^{-1}\left( \frac{x-1}{x+1} \right)[/itex]
    so that looks like arcsin. Of course, the derivative of arcsin is not cosine.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted