 Hello friends, let's work out the following problem. It says find the derivative of the following function. The given function is x upon 1 plus tan x. To find the derivative of this function we will be using quotient rule. It says d by dx of u by v is given by v into du by dx minus u into dv by dx upon v square. So this knowledge will work as t idea. Let us now move on to the solution. The given function is x upon 1 plus tan x and we have to find the derivative of this function. Here we will be using the quotient rule. Here u is x and v is 1 plus tan x. So applying the quotient rule v that is 1 plus tan x into the derivative of x minus u that is x into d by dx of v that is 1 plus tan x upon v square that is 1 plus tan x whole square. Again this is equal to 1 plus tan x into derivative of x with respect to x is 1 minus x into the derivative of 1 plus tan x. Now derivative of 1 is 0 and derivative of tan x is secant square x. So it is 0 plus secant square x upon 1 plus tan x whole square. So this is equal to 1 plus tan x minus x into secant square x is minus x secant square x upon 1 plus tan x whole square. Hence the derivative of the given function is 1 plus tan x minus x into secant square x upon 1 plus tan x whole square. So this completes the question and the session. Bye for now. Take care. Have a good day.