00:01
Hi, let's start the solution.
00:02
In this question, we have given x of t equal to 1 upon t plus 1 and y of t equal to t upon t minus 1 and t equal to 2.
00:25
As x equal to 1 upon t plus 1, that is we have t plus 1 equal to 1 by x.
00:37
So we get here t equal to 1 by x minus 1 and t minus 1 equal to 1 by x minus thus y equal to t upon t minus 1.
01:00
Put the value of t and t minus 1 here that is equal to 1 by x minus 1 divided by t minus 1 is 1 by x minus 2.
01:10
By simplifying this here, we get y equal to 1 minus x divided by 1 minus 2x.
01:20
Now we use quotient rule of differentiation to get dy by dx.
01:29
So dy by dx that is equal to dy by dx of y is 1 minus x divided by 1 minus 2x.
01:37
So here that is equal to quotient rule says that denominator square means 1 minus 2x whole square in numerator denominator as it is then dy by dx of numerator which is 1 minus x minus numerator that is 1 minus x into dy by dx of denominator that is 1 minus 2x.
02:02
So we get here that is equal to 1 minus 2x.
02:06
Differentiation of 1 minus x is minus 1 minus 1 minus x into differentiation of 1 minus 2x is minus 2 divided by 1 minus 2x whole square.
02:21
So we get here that is equal to minus 1 plus 2x and this minus minus become positive plus 2 minus 2x divided by 1 minus 2x whole square.
02:39
So by simplifying this here we get that is equal to 1 upon 1 minus 2x whole square.
02:48
So here we get dy upon dx is 1 upon 1 minus 2x whole square at t equal to 2, x is 1 upon 2 plus 1 that is equal to 1 by 3 and dy upon dx at x equal to 1 by 3 that is equal to 1 upon 1 minus 2 by 3 whole square that is equal to 9.
03:22
This is the slope m...