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: Calculus partial derivatives problem [y^(-3/2)arctan(x/y)] * *

  1. Oct 11, 2012 #1
    Calculus partial derivatives problem [y^(-3/2)arctan(x/y)] *urgent*

    1. The problem statement, all variables and given/known data

    f(x,y) = y^(-3/2)arctan(x/y)...find fx(x,y) and fy(x,y) [as in derivatives with respect to x and with respect to y].

    2. Relevant equations

    3. The attempt at a solution

    mathematics is not my strong suit..i tried the problem from a couple of different angles..i am not getting the correct answer

    here is what i have tried doing so far..i used the product rule obviously. we know that derivative of (1/a)arctan(x/a) gives (1/(a^2+x^2)

    i took y^(-3/2) as 'u' and arctan(x/y) as 'v' for the implementation of the product rule. so am i getting y/(y^2+x^2) as the derivative (since (1/y) is missing from the arctan term)?

    for fx(x,y) i get the answer y^(-1/2)/(y^2+x^2). this answer matches with the book's answer (ch-13.3 prob no.25 - calculus 9th ed by anton, bivens, davis)

    however i am not sure if i got it correct only by chance since i used the same method for fy(x,y) only to get an incorrect answer..my answer for fy(x,y) came
    -(3/2)y^(-5/2)arctan(x/y) - xy^(-5/2) / (y^2+x^2)

    the correct answer is
    -(3/2)y^(-3/2)arctan(x/y) - xy^(-3/2) / (y^2+x^2) [note: (xy^(-3/2)...not (xy^(-5/2)]

    fy(x,y) = -(3/2)(y^(-5/2))arctan(x/y) + (y^(-3/2)) (y/(y^2+x^2)) (-x/(y^2))
    which gives: -(3/2)y^(-5/2)arctan(x/y) - (xy^(-5/2)) / (y^2+x^2)
    so what went wrong there..?

    been stuck for hours its quite frustrating....so can anyone please show me the workings with the steps so that i know where i am getting it wrong?

    thanks in advance! :)
  2. jcsd
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook

Can you offer guidance or do you also need help?
Draft saved Draft deleted