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# Proving the derivative of a cross product watch

1. Show that

I can do it if I expand everything out, but given that we've just covered the permutation operator, I'm guessing that's not what we're supposed to do.

I've got but I'm not sure where to go from there? If I treat and as constants and apply the chain rule then I end up with a minus error in the answer so I'm guessing I can't treat them as constants. Could someone give a hint on where to go next?
2. (Original post by Plagioclase)
Show that

I can do it if I expand everything out, but given that we've just covered the permutation operator, I'm guessing that's not what we're supposed to do.

I've got but I'm not sure where to go from there? If I treat and as constants and apply the chain rule then I end up with a minus error in the answer so I'm guessing I can't treat them as constants. Could someone give a hint on where to go next?
Just use the definition of derivative, both and are functions so the usual applies.

then take .

Just realised I've changed the letters to something more familiar to me, I'm sure you get the idea though.
3. (Original post by Plagioclase)
Show that

I can do it if I expand everything out, but given that we've just covered the permutation operator, I'm guessing that's not what we're supposed to do.

I've got but I'm not sure where to go from there? If I treat and as constants and apply the chain rule then I end up with a minus error in the answer so I'm guessing I can't treat them as constants. Could someone give a hint on where to go next?
In index notation, you usually work on a single component at a time and then this seems to work out trivially. Haven't done this for a long time though:

I can't see where you'd pick up a -ve sign to be honest. Can you put up your working?
4. Because there seem to be differering approaches suggested, I'm going to throw my weight behind atsruser here; this should be a simple application of product rule to . I don't think there's any need to go back to formal definitions of derivatives etc.
5. (Original post by DFranklin)
Because there seem to be differering approaches suggested, I'm going to throw my weight behind atsruser here; this should be a simple application of product rule to . I don't think there's any need to go back to formal definitions of derivatives etc.
Having googled a bit, I can find no specific examples of this derivation using indices. However it's so trivial that I'll be rather depressed if there's an error with it.

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