00:01
We'll go back to number eight.
00:04
We're still in calculus three, chapter three, section two.
00:08
Question 62.
00:09
All right, so question 62 gives you a position vector, r of t.
00:19
That little arrow is means vector.
00:22
It's a function of t.
00:23
So the vector value function in three dimensions.
00:26
We have three t, i, so three t in the x direction, exact this direction, plus six l and t.
00:42
J hat and five plus five e the negative three t plus five e to the negative three t okay we're asked to find r prime or double prime and our triple prime so in other words the velocity the acceleration of the drug vectors okay so this is call it r prime now what we're going to do is we're going to differentiate component component -wise.
01:13
So 3t, differentiative suspected t, 6l &t, differential, differentiated expected t, and 5e to the negative 3t, differentiated suspected t, based on your elementary calculus background.
01:26
So the derivative 3t, the derivative 3t, the sifted t is 3 in the i direction.
01:32
I is 1 -0 -plus the derivative 6l &t is 6 times 1 over t, so 6 over t.
01:39
Now i'm going to do r double prime and all triple prime.
01:42
It might be easier to do with it if i write it is t than negative 1.
01:46
But the derivative of ln of t is 1 over t.
01:50
In the j direction, j is the unit vector long the y axis 010.
01:56
Plus, what's the derivative of the stuff? it's e to the stuff.
02:00
Chain rule times the derivative of the stuff.
02:03
It's a negative through t.
02:04
Whoops.
02:04
That's what's that.
02:09
Negative 3 .2.
02:11
There you go...