 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 x plus cos x into x minus tan x to find derivative of this function will be using product rule which says Derivative of the function u into v is given by u into dv by dx plus V into du by dx So this will be the key idea Let us now move on to the solution The given function is x plus cos x into x minus tan x. We have to find derivative of x plus cos x into x minus tan x Now let u be equal to x plus cos x and we be equal to x minus tan x Now We have to find derivative of u into v. We will use the product rule u into dv by dx plus V into du by dx Let us now substitute the values of u and v here u is x plus cos x into derivative of x minus tan x plus v that is x minus tan x into derivative of u and u is x plus cos x Now This is equal to x plus cos x and the derivative of x with respect to x is 1 and derivative of tan x is secant square x so minus tan x becomes minus secant square x plus x into x minus tan x Into derivative of x plus cos x and the derivative of x with respect to x is 1 and derivative of cos x is minus sin x Again, this is equal to x plus cos x and taking negative common negative sin common from this this becomes secant square x minus 1 plus x minus tan x Into 1 minus sin x now. We know that secant square x Minus 1 is tan square x so this becomes minus tan square x into x plus cos x plus x minus tan x into 1 minus sin x Hence the derivative of the given function is minus tan square x into x plus cos x plus x minus tan x Into 1 minus sin x And this completes the question. Bye for now. Take care. Have a good day