Can You Pull Out 1/dx in Differential Equations?

  • Thread starter Thread starter RandomGuy88
  • Start date Start date
Click For Summary
Pulling out 1/dx in differential equations is possible under certain conditions, but it is not typically favored in mathematical practice. The discussion highlights the need for functions to meet specific criteria to treat differentials as fractions. There is uncertainty about the meaning of 1/dx, with some participants questioning its validity in the context of differential equations. An example is provided to illustrate the concept, but it emphasizes that pulling out 1/dt does not imply any special significance. Overall, the conversation underscores the complexities and nuances involved in manipulating differentials in equations.
RandomGuy88
Messages
404
Reaction score
6
I am wondering if this is valid.

(de/dx) + (1/p)(dP/dx) = (1/dx)(de +(1/p)dP)

Basically are you allowed to pull a 1/dx out of the equation?
 
Physics news on Phys.org
What would 1/dx even mean?
 
Yes it is possible, although a mathematician would not like it :biggrin:. There are certain requirements the function must meet before you are allowed to treat the differentials like parts of a fraction which I don't know off the top of my head.
 
Thanks for the replies. I am not sure what 1/dx would mean. In fact that is why I am asking this question, because I didn't think it would mean anything and therefore is wrong.
 
Let's say I have {df \over dt} = 3t^2 and you just pulled out the 1/dt to get {1 \over {dt}}(df) = 3t^2. There is nothing special going on.
 

Similar threads

Undergrad Integral confusion for a simple Differential Equation
  • · Replies 2 ·
Replies
2
Views
1K
Graduate Summing over continuum and uncountable numerocities
  • · Replies 1 ·
Replies
1
Views
3K
High School Integration by Parts, an introduction I get confused with
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Multiplying divergent integrals using Hardy fields approach
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Question about Integrals to Determine Volume vs Surface Area
  • · Replies 5 ·
Replies
5
Views
3K
Undergrad Can dp/dt Be Found When p(x) Is Inverse?
  • · Replies 12 ·
Replies
12
Views
2K
High School Product rule OR Partial differentiation
  • · Replies 4 ·
Replies
4
Views
4K
Undergrad Is My Calculus of Variations Approach Correct?
  • · Replies 12 ·
Replies
12
Views
3K
Undergrad How to Find the Derivative of F = f(x)/f(x+dx)?
  • · Replies 15 ·
Replies
15
Views
2K
Undergrad Landscape Fabric Roll
  • · Replies 8 ·
Replies
8
Views
3K