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: Multi variable derivative

  1. Jun 19, 2008 #1
    whats derivative of arctan (xy) with respect to x

    3. The attempt at a solution

    - I feel kind of stupid for this one, but I can't seem to figure out the derivative here. I know with one variable that arctan goes to 1/(1+x^2), but I'm not sure what to do with two variables. please help.
  2. jcsd
  3. Jun 19, 2008 #2
    Since you know that [tex]\frac{d}{dx} \arctan x = \frac{1}{1+x^2}[/tex], you have to apply the chain rule.
    Last edited: Jun 19, 2008
  4. Jun 19, 2008 #3


    User Avatar
    Homework Helper

    The more general formulae would be [tex]\frac{d}{dx} \arctan f(x) = \frac{f'(x)}{1+f(x)^2}[/tex]. You have to use implicit differentiation and the chain rule to do this one.
  5. Jun 19, 2008 #4
    - I'm still not grasping it. We haven't really done any problems with implicit differentiation like this.
  6. Jun 19, 2008 #5

    [tex]y=\tan^{-1}{(xy)} \rightarrow y=\tan^{-1}f(x)[/tex]

    Let [tex]f(x)=xy \rightarrow f'(x)=xy'+y[/tex]


    Now you take it.
    Last edited: Jun 19, 2008
  7. Jun 19, 2008 #6
    try finding derv of
    arctan (5x)
    now substitute your y for a
  8. Jun 20, 2008 #7


    User Avatar
    Science Advisor
    Homework Helper

    Or d(arctan(xy))/dx = d(arctan(xy))/d(xy) times (d(xy)/dx). :smile:
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook