I feel this is going to turn out to be a pretty straightforward question. I just want to make sure I'm correct in my understanding of the following notation ( It just wasn't defined in class) this is from my differential geometry course.
$X_p[f]=\tfrac{d}{dt}|_{t=0}f(\alpha(t))$
Now I'm 99.99% sure this says that we simply differentiate $f(\alpha(t))$ and then find what its value is at t=0. I just want to be absolutely sure before i start my assignment.