00:01
Okay, you're trying to find the directional derivative of a function at a point in a certain direction.
00:07
So here's the formula, and you say the directional derivative of f at x, not, y, not in the u direction is, it's the gradient of f at x, not, y, not dotted with u, which is a unit vector in a certain direction.
00:30
Okay, so in your particular problem, i got that the function was the sign of x plus 2y, and that a specific point was 3 -4, but i'm a little unclear about the unit vector.
00:43
I think it's in the pi over 3 direction.
00:46
If it's not right, you can fix it from here.
00:50
Okay, so the first thing we have to do is we have to, oops, we have to find out what del f is.
00:55
So to find del f, which is a vector, remember all you do is you take the partial with respect to x, comma, partial with respect to y.
01:09
So the derivative of the sign of something is the cosine of that something times the derivative of that something.
01:17
And the derivative of x plus 2y with respect to x is 1.
01:23
And then f of y, derivative of the sign of something, cosine of the something, times.
01:30
There's the derivative of the something which with respect to y is two.
01:37
All right.
01:38
And so that's any del f for that function...