00:01
In this question, we are driven a vector r of t as t square 1 minus 2, 4t.
00:11
We need to obtain the derivative of r of t dot a of t, such that a of 6 is given by negative of 7, 4 and 7, and a dash of 6.
00:35
Is given by negative of 4, negative of 2, negative of 9.
00:42
We need to obtain this derivative at the point is equal to 6.
00:47
Now, d over dt of r of t dot a of t by using product rule is given by r of t times d over dt of dt of a plus a of t times d over d of t of r of t, that is, rt dot a -d -t plus ad dot r -d -t.
01:27
Now we need to obtain the derivative, that is, d over d -d of r of t times a of t, and point t is fidotene p as 6, so fitrotum t as 6 we get r of 6, times a dash of 6 plus a of 6 times r dash of 6.
01:54
Mark the specification 1.
01:56
Now to solve this, let us first obtain the value of r dash of 6.
02:03
For that, the given vector r of t is t squared 1 minus t times 4 t...