# Differentiatial equation

1. Jan 31, 2016

### TimeRip496

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. Jan 31, 2016

### blue_leaf77

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
$$∅*(\frac{d}{dξ})\neq \frac{d∅}{dξ}$$

3. Jan 31, 2016

### TimeRip496

Thanks!

But then how do I get from equation (12) to equation (13)? The only way I can do it is when
$$∅*(\frac{d}{dξ}) = \frac{d∅}{dξ}.$$

4. Jan 31, 2016

### blue_leaf77

Where did you get source from? Is it the same source as the one with harmonic oscillator in another thread of yours?

5. Jan 31, 2016

### TimeRip496

Yes.
Source: http://vixra.org/pdf/1307.0007v1.pdf

6. Jan 31, 2016

### blue_leaf77

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.

7. Jan 31, 2016

### TimeRip496

Ok thanks again for your help!