00:01
So in this question, we want to find the derivative of the function at the point p, not, in the direction of a vector a.
00:08
So i am finding a directional derivative this time.
00:12
I want the derivative of f of x, y, z, which is equal to xy plus y z plus z, at the point 3, negative 3, 2, 2, in the direction of the vector 6i plus 2j minus 3k.
00:27
So if i want the directional derivative of f in the direction of a given vector a, you may remember that this is equal to the gradient of f dotted with the unit vector that points in the same direction as the vector a.
00:48
So let's get our gradient vector to start.
00:51
So my gradient consists of the partial of f with respect to x, the partial of f with respect to y, and the partial of f with respect to z.
01:00
My partial with respect to x would be y plus z y plus z my partial with respect to y would be x plus z my partial with respect to y would be x plus z and then my partial with respect to z what is that going to be that's going to be y plus x and i'm going to dot this with the vector that's a unit vector pointing in the same direction as the vector a.
01:35
Well, i'm going to need the magnitude of this vector a.
01:40
It's the square root of the sum of the squares of the components.
01:43
The squared of 36 plus 4 plus 9.
01:46
The squared of 49, which is 7...