Posted by **Sarah** on Friday, June 15, 2012 at 12:16am.

Differentiate each function

a) y = Cos³ x

b) y = Sin(x³)

c) y = Sin²xCos3x

- Calculus -
**Damon**, Friday, June 15, 2012 at 2:46am
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

- Calculus -
**Damon**, Friday, June 15, 2012 at 2:49am
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

- Calculus -
**Damon**, Friday, June 15, 2012 at 2:52am
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

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