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Differentiatial equation

  1. Jan 31, 2016 #1
    Does $$ ∅*(\frac{d}{dξ})=∅*(\frac{d1}{dξ}) $$?

    If is true,
    Does multiplying a function and a derivative equals to the derivative of that function? For e.g. $$ ∅*(\frac{d}{dξ})=\frac{d∅}{dξ} $$ where ∅ is a function of ξ

    But isn't it supposed to be like this(based on the product rule), $$ ∅*(\frac{d}{dξ}) = ∅*(\frac{d1}{dξ}) = \frac{d}{dξ}*∅-1*\frac{d∅}{dξ} $$ ?

    What if ∅ is a constant or is not a function of ξ?
     
  2. jcsd
  3. Jan 31, 2016 #2

    blue_leaf77

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    Obviously no. Derivative symbol with nothing next to the right of it constitutes no meaningful quantities, no numerical value can be associated with it (if the variable is given a number), it's just an instruction to differentiate whatever stands on the right. If you put something to the right of a derivative (like you did in the RHS of that equation), you have given a numerical value to the entire expression.
    Therefore
    $$
    ∅*(\frac{d}{dξ})\neq \frac{d∅}{dξ}
    $$
     
  4. Jan 31, 2016 #3
    Thanks!
    upload_2016-1-31_19-20-24.png
    upload_2016-1-31_19-20-46.png
    But then how do I get from equation (12) to equation (13)? The only way I can do it is when
    $$
    ∅*(\frac{d}{dξ}) = \frac{d∅}{dξ}.
    $$
     
  5. Jan 31, 2016 #4

    blue_leaf77

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    Where did you get source from? Is it the same source as the one with harmonic oscillator in another thread of yours?
     
  6. Jan 31, 2016 #5
    Yes.
    Source: http://vixra.org/pdf/1307.0007v1.pdf
     
  7. Jan 31, 2016 #6

    blue_leaf77

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    I believe that's not the common and standard way to write the derivative of a function; in equation (12), ##\phi_0## should be on the right of the bracketed terms.
     
  8. Jan 31, 2016 #7
    Ok thanks again for your help!
     
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