Partial Derivative Product with variables as functions

  • Thread starter Estane
  • Start date
  • #1
4
0

Homework Statement



I'm trying to understand how a certain substitution can be made with regards to taking the partial derivative of a function product when the variable I am differentiating by is a function itself.


Homework Equations



(∂/∂p) (v(p)p(x,t)) = v(p) + (∂v/∂p)p


The Attempt at a Solution



My first thought was to use the product rule, but that seems to fall down with the function p(x,t) there. Am I missing something obvious here?
 
Last edited:

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Because the derivative is with respect to p, the fact that p is a function of x and y is irrelevent. With f(p)= pv(p), by the product rule, df/dp= v+ p dv/dp. Notice that these are ordinary derivatives, not partial derivatives, because f depends on the single variable, p.
 
  • #3
4
0
So if I'm understanding this correctly, all the derivatives should be ordinary rather than partial in this case?
 
  • #4
HallsofIvy
Science Advisor
Homework Helper
41,847
966
Yes.
 
  • #5
4
0
Ok, thank you for your help.
 

Related Threads on Partial Derivative Product with variables as functions

  • Last Post
Replies
2
Views
1K
Replies
1
Views
5K
  • Last Post
Replies
9
Views
10K
Replies
8
Views
2K
Replies
3
Views
956
Replies
3
Views
6K
Replies
4
Views
9K
  • Last Post
Replies
2
Views
1K
Top