00:01
We want to find the slope of the tangent line to the point 1 -1 on the equation x -cube plus 2xy plus y squared equals 4.
00:10
To solve this problem, we're going to use the process of 1 plus a differentiation, which from which we differentiate both sides with respect to x and solve for d -y -d -x, the rate of change of the equation, as we've listed the steps here.
00:22
Then we'll find d -y -d -d -x at that point to find the slope.
00:25
So first, differentiate every term with respect to x in its equation.
00:29
This gives us d -dx, x, x, clear, plus 2xy plus y squared equals ddx4.
00:35
On the left -hand side, we take a simple derivative, followed by the product rule, followed by another simple derivative with implicit differentiation...