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: Perhaps a simple derivative?

  1. Apr 5, 2012 #1
    1. The problem statement, all variables and given/known data

    Find the derivative of the function: q = sin ([itex]\frac{t}{\sqrt{t+1}}[/itex])

    Answer: cos ([itex]\frac{t}{\sqrt{t+1}}[/itex]) ([itex]\frac{t+2}{2(t+1)^{\frac{3}{2}}}[/itex])

    2. Relevant equations

    Chain Rule
    [itex]\frac{dq}{dt}[/itex] sin x = cos x

    3. The attempt at a solution

    [itex]\frac{dq}{dt}[/itex] = cos ([itex]\frac{t}{\sqrt{t+1}}[/itex]) [itex]\frac{dq}{dt}[/itex] (t(t+1))[itex]^{-\frac{1}{2}}[/itex] = cos ([itex]\frac{t}{\sqrt{t+1}}[/itex]) (t(-[itex]\frac{1}{2}[/itex](t+1)[itex]^{-\frac{3}{2}}[/itex] + 1(t+1)[itex]^{-\frac{1}{2}}[/itex])

    So that's as far as I've gotten with this problem. I unfortunately don't know how to continue with it though. Does simplifying the derivative of (t(t+1))[itex]^{-\frac{1}{2}}[/itex] lead me to the answer provided? Or did I derive something wrong?
  2. jcsd
  3. Apr 5, 2012 #2
    Yes, you're right simplification will lead you to the right answer.

    so you have

    -t/(2(t+1)^(3/2)) + 1/(t+1)^(1/2)

    so the common denominator is 2(t+1)^(3/2) so multiply the top and bottom of the second expression by 2(t+1)

    so you have

    -t/(2(t+1)^(3/2)) + 2(t+1)/(2(t+1)^(3/2))

    add them now


  4. Apr 5, 2012 #3
    Ah thank you! I've figured it out now and learned a new thing about exponents.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook