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## Homework Statement

My homework problem is a proof in orbital mechanics, but I'm not looking for specific help on that just yet, I'd like to work through it on my own. In doing so however, I'm having a hard time conceptualizing the idea of derivatives of vectors at a specified time. If

*is a general position vector, and*

**r***is the position vector at time*

**r**_{0}*, and the same applies for velocity vectors*

**t**_{0}*and*

**v***, it seems to me that the derivatives of each of the vectors specified at time 0 should be 0, because these values are constant. But I also don't see how that can be true because*

**v**_{0}*should be the derivative of*

**v**_{0}

**r**_{0}.## Homework Equations

*where*

**r=ar**_{0}+bv_{0}*and*

**a***are scalar functions of time.*

**b**## The Attempt at a Solution

If I attempt to take the derivative of the above equation, I'm not sure whether or not I can say the derivatives of

*and*

**r**_{0}*are 0, leaving me with*

**v**_{0}*or not.*

**v=a'r**_{0}+b'v_{0}Thanks for any help guys, sorry if this is a bit of a dumb question but it's really messing with my head right now. Cheers