00:01
In your question, we want to find the equation of the tangent line to this curve at a given point.
00:06
So what we have to do, we need two pieces of information.
00:09
We need a point, and we're going to need slope at that point.
00:16
So the slope we find by taking our derivative and finding the value of dy dx at the point 1, 1.
00:28
So let's start there.
00:29
There.
00:30
Our derivative of 18x is just going to be 18 minus, and i'm going to use parentheses here, because for this part, i have to use a product rule.
00:40
That's the first function, x, times the derivative of the second function, which is dy dx, plus the second function, y, times the derivative of the first function, which is just a 1.
00:55
We are taking the derivative with respect to x, so when we do a derivative on an x term, it's just normal.
01:02
But when we do it with a y, we have to put the symbol dy dx with our derivative.
01:09
We would then have the derivative of y squared, which is 2y dy dx.
01:16
And the derivative of 18 is a derivative of a constant.
01:20
It's just 0.
01:22
We can now plug in our x and y values and start to solve for dy dx...