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

Solution:

The given function is f(x) = (sin x + cos x)/(sin x - cos x)

Its derivative using the quotient rule is,

d/dx (f(x)) = [ (sin x - cos x) d/dx (sin x + cos x) - (sin x + cos x) d/dx (sin x - cos x) ] / (sin x - cos x)²

= [ (sin x - cos x) (cos x - sin x) - (sin x + cos x) (cos x + sin x) ] / (sin x - cos x)² (using derivative formulas)

= [ sin x cos x - sin²x - cos²x + cos x sin x -  sin x cos x - sin²x - cos²x - cos x sin x ] / (sin x - cos x)² 

= [ - 2 sin²x - 2 cos²x ] / (sin x - cos x)² 

= [ -2 (sin²x + cos²x) ] / (sin x - cos x)² 

= -2 / (sin x - cos x)² 

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 17

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

Summary:

The derivative of the given function (sin x + cos x)/(sin x - cos x) is -2 / (sin x - cos x)²