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V0ODO0CH1LD

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## Homework Statement

If u(t) = σ(t) . [σ'(t) x σ''(t)], show that u'(t) = σ(t) . [σ'(t) x σ'''(t)].

## Homework Equations

The rules for differentiating dot products and cross products, respectively, are:

d/dt f(t) . g(t) = f'(t) . g(t) + f(t) . g'(t)

d/dt f(t) x g(t) = f'(t) x g(t) + f(t) x g'(t)

## The Attempt at a Solution

So I applied each individual rule to σ(t) . [σ'(t) x σ''(t)] to get

σ'(t) . [σ'(t) x σ''(t)] + σ(t) . [σ''(t) x σ''(t) + σ'(t) x σ'''(t)]

which I can expand into

σ'(t) . [σ'(t) x σ''(t)] + σ(t) . [σ''(t) x σ''(t)] + σ(t) . [σ'(t) x σ'''(t)]

meaning σ'(t) . [σ'(t) x σ''(t)] + σ(t) . [σ''(t) x σ''(t)] should equal zero, but I don't see why it would.

Thanks