Find the derivative of the following function: (x + cos x) (x - tan x)

Solution:

The given function is f(x) = (x + cos x) (x - tan x).

Using the product rule, its derivative is,

d/dx (f(x)) = (x + cos x) d/dx (x - tan x) + (x - tan x) d/dx (x + cos x)

= (x + cos x) (1 - sec²x) + (x - tan x) (1 - sin x)   (using derivative formulas)

= (x + cos x) (-tan²x) + (x - tan x) (1 - sin x)   (as sec² - 1 = tan²x)

= -tan²x (x + cos x) + (x - tan x) (1 - sin x)

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 25

Find the derivative of the following function: (x + cos x) (x - tan x)

Summary:

The derivative of the given function (x + cos x) (x - tan x) is -tan²x (x + cos x) + (x - tan x) (1 - sin x)