00:01
To start solving this problem, we're going to take the derivative with respect to x on both sides.
00:05
So we'll take d, d, d, x, of this x, y, plus one, cubed, and this is equal to the derivative with respect to x of x minus y squared plus 8.
00:17
Now, on this side here, we're going to take the derivative of this, and we're going to need to use chain rule.
00:22
So we're going to have three times x, y, plus one, squared, and then from chain rule, we're going to take the derivative.
00:31
Of the inside part, which is xy plus 1.
00:35
On the right -hand side, we'll go ahead and take the derivative of this, which is just 1, and then the derivative of this, we're going to have minus 2y and then times d -y -d -x because of chain rule.
00:49
So i'll have minus 2y times d -y -d -x, and then the derivative of this is just going to be a constant, so that's going to just be 0.
01:03
Now, finding this derivative here, so we'll have 3 times x, y, plus 1 squared.
01:12
On this part here, we're going to need to use product rule.
01:16
So product rule says that it's going to be first times derivative of the second, which is x times dy, dx, and then plus second times derivative first.
01:28
So y times 1.
01:30
So that's going to be plus y, like so.
01:32
And this is going to be equal to.
01:34
Oh, and then the derivative of the 1 is just a constant, or it's just a constant, so it's just going to be 0...