# Time derivatives where there's no explicit time dependence

1. Mar 18, 2007

### Pythagorean

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?

2. Mar 18, 2007

### Mute

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).

3. Mar 18, 2007

### Pythagorean

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