 Hello and welcome to the session. Let us understand the following question today. If x is equal to under root a to the power side inverse t, y is equal to under root a to the power cos inverse t, show that dy by dx is equal to minus y by x. Now let us write the solution. Consider x is equal to under root a to the power side inverse t. Therefore dx by dt is equal to 1 by under root 2 multiplied by under root a to the power side inverse t, multiplied by dy dt of a side inverse t, which is equal to 1 by 2 into a to the power side inverse t, multiplied by a high inverse t, log a multiplied by 1 by under root 1 minus t square. Now consider y is equal to under root a to the power cos inverse t. Therefore dy by dt is equal to 1 by 2 multiplied by under root a to the power cos inverse t, multiplied by dy dt of a to the power cos inverse t, which is equal to 1 by 2 multiplied by under root a to the power cos inverse t, multiplied by a to the power cos inverse t, log a multiplied by minus 1 by under root 1 minus t square. Now by chain rule dy by dx is equal to dy by dt multiplied by dt by dx which is equal to dy by dt is equal to this. So we write here minus a to the power cos inverse t, log a multiplied by 2 under root a to the power cos inverse t multiplied by under root 1 minus t square multiplied by dt by dx which is the inverse of dx by dt. So we get here under root 1 minus t square multiplied by 2 into under root a to the power sin inverse t divided by a to the power sin inverse t log a. Now we see that this log a and log a gets cancelled. This 2 gets cancelled with this 2 and under root 1 minus t square and under root 1 minus t square gets cancelled. So we are left with minus under root a to the power cos inverse t multiplied by square multiplied by under root a to the power sin inverse t whole divided by under root a to the power cos inverse t multiplied by under root a to the power sin inverse t the whole square. Here we can see that a to the power cos inverse t can be written as under root a to the power cos inverse t the whole square. Now here this gets cancelled with this and this gets cancelled with this. So we are left with minus under root a to the power cos inverse t divided by under root a to the power sin inverse t which is equal to under root a to the power cos inverse t is equal to y. So minus y divided by and under root a to the power sin inverse t is equal to x. So it is equal to minus y by x. Hence dy by dx is equal to minus y by x. Hence proved. I hope you understood the question. Bye and have a nice day.