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!

Derivatives of arctan((x+y)/(1-xy))

  1. Jul 30, 2011 #1
    1. The problem statement, all variables and given/known data

    Find all second partial derivatives of
    z=arctan((x+y)/(1-xy))


    2. Relevant equations

    d/dx of arctan(x) is 1/(1+x^2)


    3. The attempt at a solution

    Not sure how to proceed... I don't want the answer, just an idea as to how to move forward.

    My attempt at finding the first derivative...

    z'=(1/(1+(x+y/(1-xy)) * (x(1-xy) - (x+y(-y)) / (1-xy)^2

    Is this correct? If it is, I honestly don't know how to find the second derivative...

    On another note, can someone tell me how I can use math notation instead of plain text, to make the equations and such easier to read? Thanks guys.
     
  2. jcsd
  3. Jul 30, 2011 #2

    ehild

    User Avatar
    Homework Helper
    Gold Member

    Take care of the parentheses. Check the derivative of the arctan function.

    To make your task easier, remember the addition formula :
    [tex]tan(\alpha+\beta)=\frac{tan(\alpha)+tan(\beta)}{1-tan(\alpha)tan(\beta)}[/tex]
    Can you write the function z(x,y) in a simpler form?
    As for Math notations, go to "advanced" and click on the 'Σ'.
    ehild
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Derivatives of arctan((x+y)/(1-xy))
Loading...