# Calculus

posted by Sarah

Differentiate each function

a) y = Cos³ x

b) y = Sin(x³)

c) y = Sin²xCos3x

1. Damon

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

2. Damon

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

3. Damon

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

## Similar Questions

1. ### trigo help!

1. differentiate cos(3/x) 2. differentiate sin(4/x) 3. differentiate 3/{sin(3x+pi)} 4. differentiate pxsin(q/x)where p and q are constants. 5. differentiate xsin(a/x) where a is constant 6. differentiate sec^3(3x^2+1)
2. ### Calculus

Differentiate the following function. f (x) = 7 sin(x) + 1/6 cot(x)
3. ### calculus

Differentiate the following function. f (x) = 6 x 2 sin(x)tan(x) Where do I begin?
4. ### Calculus

How would you differentiate each function?
5. ### Maths - Calculus

Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand?
6. ### Maths - Calculus

Can anyone help with this...I need to find the derivative of the functions below. If possible please show working so I can try and understand?