00:01
So if we want to find the partial derivative of this, remember what we're going to do is just take the derivative like we normally would, but then all other variables we assume are constant.
00:13
So we would treat them just like any other constant in the single variable case for derivatives.
00:20
So first we do del by del x.
00:23
So that would give us del f by del x, which will often write as f sub x.
00:31
And then over here to take the derivative of natural log of something, we first would do one over the thing on the inside.
00:37
And then we apply chain rule.
00:39
So we're going to do del by del x of what was on the inside.
00:43
So x squared plus y squared plus z squared.
00:46
And now remember this y and this z here, we assume they're constant.
00:50
So if i square a constant, they're still a constant.
00:52
And if i take the derivative of a constant, that's just going to be zero in each case.
00:57
And then to take the derivative of x squared, we just use power rule.
00:59
So that would be 2x.
01:02
So that would give us 2x over x squared plus y squared plus z squared...