Find the derivative of the following function: (x² cos(π/4)) / sin x

Solution:

The given function is f(x) = (x² cos(π/4)) / sin x.

Its derivative using the quotient rule is,

d/dx (f(x)) = [ (sin x) d/dx (x² cos(π/4)) - (x² cos(π/4)) d/dx (sin x) ] / (sin x)²

= [ (sin x) (2x cos cos(π/4)) - (x² cos(π/4)) (cos x) ] / sin² x   (using derivative formulas)

= [ x cos(π/4) (2 sin x - x cos x) ] / sin² x (or)

= [ x (2 sin x - x cos x) ] / (√2 sin² x)   (Using trigonometric table, cos(π/4) = 1/√2)

NCERT Solutions Class 11 Maths Chapter 13 Exercise ME Question 27

Find the derivative of the following function: (x² cos(π/4)) / sin x

Summary:

The derivative of the given function (x² cos(π/4)) / sin x is [ x cos(π/4) (2 sin x - x cos x) ] / sin² x (or) [ x (2 sin x - x cos x) ] / (√2 sin² x)