Find the derivative of the following functions (it is to be understood that a, b, c, d are fixed non-zero constants): (a + b sin x)/(c + d cos x)

Solution:

The given function is f(x) = (a + b sin x)/(c + d cos x).

Its derivative using the quotient rule is,

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

= [ (c + d cos x) (0 + b cos x) - (a + b sin x) (0 - d sin x) ] / (c + d cos x)² (using derivative formulas)

= [ bc cos x + bd cos²x + ad sin x + bd sin²x] / (c + d cos x)²

= [ bc cos x + bd (cos²x + sin²x) + ad sin x] / (c + d cos x)²

= [ bc cos x + ad sin x + bd ] / (c + d cos x)²   (As cos²x + sin²x = 1)

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 20

Find the derivative of the following functions (it is to be understood that a, b, c, d are fixed non-zero constants): (a + b sin x)/(c + d cos x)

Summary:

The derivative of the function (a + b sin x)/(c + d cos x) is [ bc cos x + ad sin x + bd ] / (c + d cos x)²