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)) + (

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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 1 (17.1 KiB) Viewed 65 times

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).