# Time derivatives where there's no explicit time dependence

Gold Member

## 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?

Mute
Homework Helper
You use the multivariate chain rule:

$$\frac{d}{dt}f(\theta,\phi) = \frac{\partial f}{\partial \theta}\frac{d \theta}{dt} + \frac{\partial f}{\partial \phi}\frac{d \phi}{dt}$$

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).

Gold Member
ah, thank you much, that's exactly what I was looking for.