00:01
Gives us a function of three variables and asks us to compute this function's gradient.
00:07
So the function is x squared plus y squared plus z squared to the negative half power.
00:11
We're going to keep it like that because it'll be nice for taking partial derivatives.
00:16
The gradient of v is going to be v.
00:19
X, fee sub y, f sub z.
00:21
What do these mean? fee sub x is a shorthand for the partial derivative of fee with respect to x.
00:27
D sub y is a shorthand of partial derivative of y with respect to partial derivative of f with respect to y and c sub z is also shorthand for the partial of c with respect to z.
00:38
The partial with respect to x, we have to use the chain rule here up in this function.
00:45
First, we have to take this negative half and then bring it down and then subtract one from it.
00:49
So we have negative half times our entire thing again to the negative three halves power, because negative 1 half minus 1 is equal to negative 3 halves.
01:00
Then we have to multiply by the partial derivative with respect to x.
01:05
Well, these y squared plus z squared, the partial derivative is 0...