Differentiate each function

Question

a) y = Cos³ x

b) y = Sin(x³)

c) y = Sin²xCos3x

Answer 1

a)
let z = cos x then dz/dx = -sin x
y = z^3
y' = 3 z^2 dz/dx
y' = 3 cos^2 x (-sin x)
= -3 sin x cos^2 x

Answer 2

b)
let z = x^3 then dz/dx = 3 x^2
y = sin z
y' = cos z dz/dx
= cos(x^3) (3 x^2)
= 3 x^2 cos x^3

Answer 3

c)y' = sin^2 x (-3sin 3x)+ cos 3x (2 sin x cos x

= -3sin 3x sin^2 x + 2 cos 3x sin x cos x