 Hello friends let's work out the following problem it says find the derivative of the following function. The given function is x plus secant x into x minus tan x. To find the derivative of this function we will be using product true according to which derivative of the function u into v is given by u into dv by dx plus v into du by dx and this will be the t idea. Let us now move on to the solution. The given function is x plus secant x into x minus tan x and we have to find derivative of this function. We will use the product rule to find derivative of this function where u is x plus secant x and v is x minus tan x. So u remains as it is x plus secant x into d by dx of x minus tan x plus v that is x minus tan x into d by dx of u that is x plus secant x which is again equal to x plus secant x into d by dx of x minus d by dx of tan x plus x minus tan x into d by dx of x plus d by dx of secant x. Again this is equal to x plus secant x and derivative of x with respect to x is 1 minus d by dx of tan x. Derivative of tan x is secant square x plus x minus tan x into derivative of x with respect to x is 1 plus derivative of secant x is secant x into tan x. So this is the derivative of the given function that is x plus secant x into 1 minus secant square x plus x minus tan x into 1 plus secant x into tan x and this completes the question. Bye for now. Take care. Have a good day.