00:01
In this problem, we have been given the equation of the curve that is y is equal to 2x by x plus 1.
00:07
And we need to determine the equation of the tangent at the point p11.
00:14
So in this case, let's say this is the curve.
00:17
And we have the point p that is 1 -1.
00:21
And the tangent here will touch this curve exactly at the at one point.
00:26
So in that case, it will be better if we know the slope of this tangent.
00:31
And we know that the slope of a tangent is given by the differentiation of y with respect to x.
00:38
And once we get this slope, we can just connect with the two points, 1 -1 and x -y, and related with the slope.
00:47
So first let's determine the slope here.
00:49
So for that, we will differentiate y with respect to x.
00:52
So that will be d by dx of 2x by x plus 1.
00:57
So here we observe that this is a fraction and basically this is in the form of two functions.
01:03
So if we differentiate u by v, then in that case the formula here is u -dash v minus uv -dash divided by v square.
01:14
So when we apply this formula, we get m is equal to.
01:19
First we differentiate the numerator.
01:21
So differentiation of 2x that will be 2.
01:24
We multiply with the denominator, we subtract, and we put the numerator that is 2x, and we multiply with the differentiated form of denominator, that is 1, and divided by the square of the denominator...