00:01
So in this question, we're given a curve parameterized by r of t.
00:04
And we're given another curve, a of t, for which we know that a of 9 is 46 minus 3.
00:10
A prime of 9 is minus 7, 4 minus 1.
00:13
And we're asked to calculate the derivative of the inner product between the two at t equals n.
00:19
So of course, just recalling the formula.
00:22
So ddt of the product, you have leibniz rule, right? so it's the derivative of the first one dotted with the second one, plus the first one.
00:31
Dotted with drift of the second, right? and r prime of t here, let's make the calculation.
00:39
I want to use your brackets.
00:41
So i have t squared, so it's 2t, 1 minus t minus 1, 4t is 4.
00:48
So when we evaluate these things at t equals 9, r of t dot 80, i see what we get.
00:57
So we had r prime of 9, so 18 minus 1, 4, dotted with 8...