00:01
This problem, we are given the shown information and asked to provide the directional derivative of g.
00:06
And so our first step in doing this is going to be to find the partial of g with respect to p and the partial of g with respect to q.
00:15
And so to do this, we are going to treat q as a constant in order to find the partial with respect to p.
00:28
And so when we do this, our derivative is going to be 4 p cubed minus 2.
00:35
2p times q cubed.
00:40
And now we're going to find the partial of g with respect to q.
00:48
And that is going to be equal to negative.
00:53
So we ignore p to the fourth because we're treating p as a constant and the derivative of a constant is zero.
00:59
And so we're going to get negative p squared times 3 q squared.
01:06
And we're going to evaluate these two derivatives at the point given.
01:10
And so when we evaluate the first one at 2 .1, we're going to get 4 times 2 cubed, which is 8, minus 2 times 2 times 1, which is just 1.
01:27
And so we're going to get 4 times 8 is 32 minus 2 times 2 times 1, which is 4.
01:32
We're going to get 32 minus 4, that's 28...