00:01
Here we're given two matrix functions a and b and we want to show what the derivative of a times b is.
00:07
To do so we'll only look at a specific element.
00:14
So definition here, so we still carry the derivative, then we have the sum k equals 1 up to n of a sub ik times b of k j.
00:33
Now we can bring the derivative inside as this.
00:38
So we have a sum here, it's going to be the sum it's k equals 1 up to n d over dt.
00:46
Now remember that a sub ik simply lowercase a sub ik of t and likewise for b.
00:59
And now these are just, now these are functions that of real, these are real value functions so we can take the derivative of them.
01:10
The sum from k equals 1 up to n.
01:14
Now utilizing the product rule, we have a sub ik of t b sub k j prime of t plus a sub ik prime of t b sub k j of t.
01:36
Now we have the sum of sums, we can split up the sum...