00:01
In this question, we need to find the equation of tangent to the curve, y is equal to x minus 1 over x plus 1.
00:09
At the point, x is equal to 2.
00:12
Now, let us first obtain the slope of the tangent.
00:17
For that, differentiate the given function with respect to x.
00:21
We get dy over d x is equal to d over d x of x minus 1 over x plus.
00:30
Using the portion rule, the derivative is given by denominator d over dx of numerator minus numerator d over d x of denominator over d x of denominator over denominator over denominator square.
00:51
Solving this we get x plus 1 times 1 minus x minus 1 times 1 over x minus 1 times 1 over x plus 1.
01:02
Whole square.
01:06
Multiplying we get x plus 1 minus x plus 1 over x plus 1 whole square.
01:16
Now positive x is cancelled out with negative x and we are left with 2 over x plus 1 whole square.
01:25
This is the value of d over d x of y.
01:30
That is this is the value of slope m.
01:34
Now at the point x is equal to 2, the slope would be 2 times of 2 plus 1 whole square, that is 2 over 3 whole square.
01:51
This gives the value of slope as 2 over 9...