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Homework Help: Calculus question w/answer

  1. Apr 7, 2005 #1
    hi,

    Below i have attched both my question and answer. Can someone please take a look and tell me if its right? Thanks in advance!
     

    Attached Files:

  2. jcsd
  3. Apr 7, 2005 #2
    anyone please and thank you!
     
  4. Apr 7, 2005 #3
    Looks absolutely fine to me. Good work.

    A bit weird that there is a t on the top and bottom at the start though.

    Interesting method of notation too. I always used write in extra u's and v's for the quotient differential, etc. but you've kept it in y's and t's
     
  5. Apr 7, 2005 #4
    His notation is wrong (or at least, not consistent with any sort of standard mathematical notation).

    [tex]y = f(x) \Longrightarrow \frac{dy}{dx} = \frac{d}{dx} f(x) \neq \frac{dy}{dx}f(x),[/tex]

    (unless [itex]f(x)[/itex], and hence [itex]y[/itex], is constant)
     
    Last edited: Apr 7, 2005
  6. Apr 7, 2005 #5
    so how is it suppose to be? i dont get you
     
  7. Apr 7, 2005 #6
    On line 2, on the right hand side where you have the fraction dy/dt, tehre should not be a y. It should be

    [tex] \frac{d}{dt} (\frac{t-6}{t+6}) [/tex]
     
  8. Apr 7, 2005 #7
    You did it more than once,

    dy/dt implies the derivative of th eoriginal function, which isnt what your doing in every step, you are taking a derivative of a single term inthe function, hence (d/dt) not (dy/dt)
     
  9. Apr 7, 2005 #8
    Look at my last post, then look at your work.

    [tex]\frac{dy}{dx}f(x)[/tex]

    means that you are multiplying the derivative of [itex]y[/itex] by [itex]f(x)[/itex]. On the other hand,

    [tex]\frac{d}{dx}f(x)[/itex]

    means that you are taking the derivative of [itex]f(x)[/itex].
     
  10. Apr 7, 2005 #9
    thanks guys..got you
     
  11. Apr 8, 2005 #10
    Also the last line should read "dy/dt = ..." and not "dy/dx = ...".
     
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