# some help with this notation.

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.

• Yes, that's how I would read that right hand side too. – Jaap Scherphuis Oct 19 '18 at 12:26
• Excellent , thank you :) – excalibirr Oct 19 '18 at 12:26
• I will add that $\alpha(t)$ is any curve such that $\alpha(0)=p$ and $\alpha'(0)=X_p.$ – mfl Oct 19 '18 at 12:57