00:01
In this problem, we will cover the differential of two variable function.
00:05
So i have written in green the general equation for a differential.
00:10
So we know that in the context of this problem, we will be finding the partial derivatives of the function g with respect to u and v.
00:21
So i will start with the partial derivative with respect to u, and that's just taking the derivative holding v fixed.
00:28
So we will get 2u plus v, and we want the partial derivative of perspective v, and that's just taking the derivative holding u fixed.
00:39
And this is going to give us just u.
00:43
So now that we have our partial derivatives, we can write out our differential, and that's going to be df equals to u plus v, d, u, wait, my mistake, this is not enough, it's a g, plus u times d, v, and there goes our differential.
01:11
So now we want to estimate the change between the two given points, and to do that, we can expand our differential to look like this...