00:01
In this problem, it has said that the slope of the tangent line to the curve y is equal to 2 over x at the point 5 comma 2 over 5 is what.
00:13
So we want to find the slope of the tangent line.
00:16
And to do that, all we need to do is find the value of the derivative at the point 5, 2 over 5.
00:23
So first of all, let's find the derivative.
00:24
So we have 2 times the derivative of 1 over x, that is negative 1 over x squared.
00:30
So this is our derivative.
00:32
And we want to find the value of this derivative when x is 5, because the point is 5, 2, 2 over 5.
00:39
So, x is 5.
00:40
So we end up with negative 2 over 5 squared.
00:43
That is equal to negative 2 over 25.
00:47
So this is a required answer.
00:48
It will be negative 2 over 25.
00:51
And next we want to find the equation of the tangent line in the form y is equal to mx plus b, where m is what and b is what...