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!

Differentiation anomoly-in need of setting straight!

  1. May 7, 2007 #1
    Differentiation anomoly--in need of setting straight!

    I was studying for the AP calculus exam when I came accross this question, which seems to have multiple answers. I cannot seem to find what is wrong with it (nor can my calc teacher).

    Find dy/dx if x + y = x * y

    I went about this problem the "easy way out". Instead of implicitly differentiating, I figured I could do some algebra to simplify it to y = x / (x-1). I saw the answers, and only one of them did not have a "y" in the answer, so I picked that one. It was wrong.

    When solved implicitly, a different answer is found: (y-1)/(1-x). This is STILL different than what our answer key has, which is (1-y)/(x-1).

    Can someone please help resolve this? Thanks!
     
  2. jcsd
  3. May 7, 2007 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    What ever other problems you're having:

    contains a mistake on your part. The two answers written there are the same.
     
  4. May 7, 2007 #3
    If you differentiate [tex]y=\frac{x}{x-1}[/tex], you get [tex]\frac{dy}{dx}=\frac{(x-1)-x}{(x-1)^2}[/tex].

    Divide by [tex]\frac{x-1}{x-1}: \frac{dy}{dx}=\frac{1-\frac{x}{x-1}}{x-1}[/tex]

    Substitute [tex]y=\frac{x}{x-1}[/tex]: [tex]\frac{dy}{dx}=\frac{1-y}{x-1}[/tex]
     
  5. May 7, 2007 #4

    Office_Shredder

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    No.... it's just negative on the top and bottom. Multiply your answer by 1 = -1/-1 and see what you get
     
  6. May 7, 2007 #5

    AlephZero

    User Avatar
    Science Advisor
    Homework Helper

    Isn't implicit differentiation "the easy way"?

    1 + dy/dx = y + x dy/dx

    1-y = (x-1)dy/dx

    dy/dx = (1-y)/(x-1)
     
  7. May 7, 2007 #6
    What I meant is that, because I could see that it simplified to y = *stuff with no y*, I figured that dy/dx MUST not have a y in it. There was only one choice without one, so I chose that. It was the easy way out because I did not do any differentiating at all.

    Also, I figured out my problem. Both answers were the same, but had a "y", and the other did not. When a substitution was made for "y", the answers were identical.

    And yeah... I can't believe I didn't notice that the answer simply divided by a factor of (-1). Wow I feel dumb! :-p


    All here is well, thank you for the help.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Differentiation anomoly-in need of setting straight!
Loading...