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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.

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

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