00:01
In this question, we are asked to find an equation of the tangent line to the graph of f at the given point.
00:07
And to do that, we need to differentiate both sides of the equation implicitly.
00:14
That means that we will assume that y depends on x.
00:19
And x is the independent variable.
00:22
And that simply means that we differentiate x as usual, but whenever we differentiate y, we need to multiply it by dy or d x.
00:30
For example, the derivative of y squared equals to 2y, and we need to multiply it by dy over dx because it depends on y.
00:40
Because it involves y.
00:43
Next, the next term we differentiate as usual.
00:46
We will use the chain rule.
00:49
We will differentiate the cube first.
00:54
We will get 3 times 1 plus x cubed squared.
00:57
And then multiply by the derivative of the expression inside the cube.
01:01
And that's going to be 3x squared.
01:04
On the right -hand side, we need to use the product rule.
01:09
By the product rule, we need to differentiate x first and multiply by y, then add x multiplied by the derivative of y, which is 1, but since we are differentiating y, we need to multiply by d -y over dx...