00:01
So in this question, we want to find the directional derivative of the function g of uv equals u squared e to the negative e at the point 80 in the direction of the vector 3i plus 4j.
00:14
So let's see.
00:16
How do i get my directional derivative of a function g in the direction of a unit vector u? my formula is i'm supposed to take the gradient of g and dot it with my unit vector.
00:34
So let's get our gradient of g.
00:37
So my gradient of g consists of the partial of g with respect to the variable u and the partial of g with respect to the variable v.
00:48
My partial with respect to u looks like it would be 2u, e to the next, negative v.
00:57
While my partial with respect to v, it should be negative u squared, e to the negative v power.
01:07
Now, i need to evaluate this at the point in question, which is the point eight zero.
01:15
So if i plug in eight for you and zero for v, i'm getting 16e to the zero, followed by negative, that's 64, right, u squared.
01:29
So negative 64, e to the 0.
01:35
Looks like i'm getting 16 comma negative 64...