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# Vector Calculus watch

1. Given x = z(t), y = y(t) and z = f(x,y)
where r = x(t)i + y(t)j

Using the chain rule,

Now,
Then,

Now do vector dot products.

Rearranging,

So, I've managed to get dz/dt from the chain rule to equal grad(z*r') - almost - except for that last term

How do I get rid of that ?
2. Do you mean x=z(t) and not x(t)?

And what does z*r' mean?
3. It would make far more sense if it were dz/dt = Grad(z)*r' . Then it is a case, with cartesian Grad, of establishing the total derivative using the dot product.
4. Yep, that's it folks. Alles klar.
Many thanks.

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