[western50]

⋅ here means dot product
Here is a less coordinate-dependent "proof" of the same formula, (x(t)⋅y(t))=x(t)⋅y'(t)+x'(t)⋅y(t)... (1):

For small values of h, we have x(t + h) ≈ x(t) + hx'(t);
and similarly y(t + h) ≈ y(t) + hy'(t):
So for small h,
x(t + h)⋅y(t + h) ≈(x(t) + hx'(t))⋅(y(t) + hy'(t))
≈ x(t)⋅y(t) + h(x(t)⋅y'(t) + x'(t)⋅y(t));

and so
(x(t + h)⋅y(t + h)- x(t)⋅y(t))/h ≈ x(t)⋅y'(t) + x'(t)⋅y(t).

Taking the limit as h --> 0, the approximately equals sign "≈" changes into "=", and we get (1), which is the expression at the beginning.

So, I need to make this "proof" into a proof. In particular, your argument should use limits in a rigorous way, and not require making use of the ≈ symbol, and please give me help on how to do this problem because I really have no idea...

[galactus]

Obviously, you did not use 'preview' to see that your post did not display correctly.

If this was copy and pasted, then that is the reason.

[Unknown008]

Unfortunately, there is no preview feature in the GO skin :(

western50, can you re-type your question manually, and if you can learn use the LaTeX and use them in your posts, that would be most helpful in such cases.

[western50]

There is no typo in the whole problem, I did not just copy and paste, I typed it up.

[galactus]

It is not displaying correctly on my end. I see a bunch of squiggly nonsensical symbols. LaTex would be the ticket. For one, your 'approximately' sign is not showing.