Exercise 3. Let a: I + R", and 8: J + R" be a pair of differentiable curves. Show that (act), 8(t))) = (a'(t), 8(t)) + (
Posted: Tue Sep 07, 2021 7:23 am
Exercise 3. Let a: I + R", and 8: J + R" be a pair of differentiable curves. Show that (act), 8(t))) = (a'(t), 8(t)) + (at), 8(t)) and (lact)n)' = (ext), a't)) a(t)|| (Hint: The first identity follows immediately from the definition of the inner- product, together with the ordinary product rule for derivatives. The second identity follows from the first once we recall that || || := (-;-)1/2).