00:02
Okay, so we want to find the equation for our tangent line.
00:05
So we're given a point, and we're also going to need to find a slope.
00:09
And once we found our slope, we can plug that into our point slope form to solve for our equation of our tangent line.
00:18
Okay, so let's begin by finding our slope.
00:20
So we'll take our derivative here.
00:25
So what is that? that's 1 over x squared plus y squared times the derivative of our inside.
00:33
So that's 2x plus 2y, and it's 2.
00:36
Nty over tx, well that's equal to 1 over 5x times the derivative of our inside.
00:46
So that's this 5.
00:53
Okay, so we just get 1 over x plus the derivative of the falling.
00:59
So we're going to use our product rule.
01:01
So we have x inverse and then ty over tx plus the derivative of x to the power of negative 1.
01:08
So that's, we bring down a negative 1.
01:12
And then we have x to the power of negative 2.
01:16
And y and then the derivative of our constant that's just zero okay and now we'll multiply out or this term here so what do we get we get the following plus 2y over x squared plus y squared d y over t x okay and then we have the same thing on our right hand side okay and now we want to isolate our gy over t x so we'll multiply this on our left hand side or move this to our left hand side and then move this term to our right hand side.
01:54
Okay, so that gives us the following.
01:57
We can now factor out a d -y over d -x on our left -hand side and we're left with 2y over x squared plus y squared and a negative x in power of negative 1...
