00:01
Here we're given the equation x times y is equal to 72.
00:04
And we want to look at the point negative 8 comma negative 9.
00:07
We're going to use implicit differentiation to find the slope at this point.
00:12
Now the key to implicit differentiation is remember, y is a function of x, and its derivative is y prime, whereas the derivative of x is just one.
00:21
So here we have two functions of x multiplied.
00:25
So it's a product rule.
00:26
So i'm going to take the derivative of the first, which is one, derivative of x, times the second unchanged, plus the first unchanged times the derivative of the second.
00:35
So i'm just going to write y prime, since we don't know what the derivative of y is.
00:40
Equals the derivative of 72 is a constant, so that's just zero...