Time derivatives where there's no explicit time dependence

  • #1
Pythagorean
Gold Member
4,292
278
Say I have a funciton sin(theta - phi)

theta and phi are both time-dependant. How do I take the time derivative of this function? Is there a general notation or do I have to assume theta = w1t and phi = w2t and go with that?
 

Answers and Replies

  • #2
Mute
Homework Helper
1,388
10
You use the multivariate chain rule:

[tex]\frac{d}{dt}f(\theta,\phi) = \frac{\partial f}{\partial \theta}\frac{d \theta}{dt} + \frac{\partial f}{\partial \phi}\frac{d \phi}{dt}[/tex]

Of course, you do then need to know the time derivatives of theta and phi. (Note that this also assumes theta and phi are functions of time only).
 
  • #3
Pythagorean
Gold Member
4,292
278
ah, thank you much, that's exactly what I was looking for.
 

Related Threads on Time derivatives where there's no explicit time dependence

Replies
15
Views
305
  • Last Post
Replies
10
Views
2K
  • Last Post
Replies
1
Views
703
Replies
4
Views
6K
Replies
2
Views
988
Replies
11
Views
2K
  • Last Post
Replies
6
Views
2K
H
Replies
4
Views
1K
Top