Question

Find the derivative of following functions w.r.t. x: sin³ x. sin 3x.

Answer 1

Let y = sin³ x. sin 3x.

= 12 sin³ x . cos x – 24 sin⁵ x cos x

= 12 sin³ x cos x (1 – 2 sin² x)

= 12 sin³ x cos x . cos 2x

= 6 sin² x . 2 sin x . cos x . cos 2x

= 6 sin² x . sin 2x . cos 2x

= 3 sin² x . 2 sin 2x . cos 2x

= 3 sin² x sin 2(2x)

= 3 sin² x . sin 4x.