 Hello and welcome to the session. Let us discuss the following question. It says find the derivative of the following function. The given function is secant x minus 1 upon secant x plus 1. To find the derivative of this function, we'll be using quotient rule. It says derivative of the function u by v with respect to x is given by v into du by dx minus u into dv by dx upon v square. So this knowledge will work as key ideal. Let us now move on to the solution. We have to find the derivative of function secant x minus 1 upon secant x plus 1. Now, we'll find the derivative of this function using quotient rule. So for convenience, let u be equal to secant x minus 1 and v be equal to secant x plus 1. Now, we find the derivative of this function by the quotient rule v into du by dx minus u into dv by dx. Let us now substitute the values of u and v in this. So this becomes equal to v is secant x plus 1 into du by dx that is dy dx of u which is secant x minus 1 minus u which is secant x minus 1 into d by dx of v that is secant x plus 1 upon v square which is secant x plus 1 whole square. Now this is equal to secant x plus 1 into d by dx of secant x minus 1. Now the derivative of secant x is secant x into tan x and the derivative of 1 is 0 minus secant x minus 1 into dy dx of secant x plus 1. Now the derivative of secant x is secant x into tan x and the derivative of 1 is 0 upon secant x plus 1 whole square. Again, this is equal to secant x into secant x into tan x is secant square x into tan x plus 1 into secant x into tan x is secant x into tan x minus secant x into secant x into tan x is secant square x into tan x minus 1 into secant x into tan x is minus secant x into tan x upon x plus 1 whole square. Again, this is equal to secant square x into tan x plus secant x into tan x opening the brackets It becomes minus secant square x into tan x plus secant x into tan x upon secant x plus 1 whole square. Now secant square x into tan x gets cancelled with minus secant square x into tan x and we have secant x into tan x plus secant x into tan x is 2 secant x tan x upon secant x plus 1 whole square. Hence, the derivative of the given function is 2 secant x into tan x upon secant x plus 1 whole square. And this completes the question. Bye for now. Take care. Have a good day.