Time derivatives where there's no explicit time dependence

  • #1
Pythagorean
Gold Member
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255

Main Question or Discussion Point

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
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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
4,191
255
ah, thank you much, that's exactly what I was looking for.
 

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