00:01
To find the slope of the tangent line, we first need to find the derivative of the function.
00:08
So here, f of x is equal to x over x plus 6.
00:12
Let's go ahead and find the derivative.
00:15
So i have f prime of x is equal to.
00:19
Okay, i need the derivative of the numerator, which is just one.
00:26
And then i need the second function or the denominator, which is x plus 6, minus the first.
00:36
Function, which is the numerator, which is x, and then the derivative of the second function, or the denominator, which is just one, all over six, sorry, x plus six squared.
00:59
Okay, from here, let's go ahead and simplify.
01:04
So i have f prime of x is equal to x plus six minus x.
01:14
All over x plus 6 in the quantity squared.
01:21
Let's combine like terms.
01:23
I see a positive x and a negative x.
01:25
So really, those just cancel out.
01:28
And i'm left with 6 over x plus 6.
01:33
Parthesis squared.
01:37
Now to find the slope of the tangent line, i need to look at the points that they gave me.
01:44
Okay, in this problem, they gave me the point 3 comma 1.
01:49
One third.
01:52
Again, think of this as x comma y.
01:55
I want to use the x value and plug it into the derived function that i just found.
02:03
So again, i'm finding the slope of the tangent line...