Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): cos x/(1 + sin x)

Solution:

The given function is f(x) = cos x/(1 + sin x).

Its derivative using the quotient rule is,

d/dx (f(x)) = [ (1+sin x) d/dx (cos x) - cos x d/dx (1+sin x) ] / (1 + sin x)²

= [ (1+sin x) (- sin x) - cos x (0 + cos x) ] / (1 + sin x)² (using derivative formulas)

= [ - sin x - sin²x - cos²x ] / (1 + sin x)²

= [- sin x - (sin²x + cos²x) ] / (1 + sin x)²

= [- sin x - 1] / (1 + sin x)²    [As sin²x + cos²x = 1]

= -(1 + sin x) / (1 + sin x)²

= -1 / (1 + sin x)

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 16

Find the derivative of the following functions (it is to be understood that a,b,c,d,p,q,r and s are fixed non-zero constants and m and n are integers): cos x/(1 + sin x)

Summary:

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