Trying to differentiate using function of a function/Chain rule

[Mike2793]

Homework Statement

Using the function of a function formula differentiate the following:

y = (cos 2x)³

Homework Equations

dy/dx = dy/du * du/dx

The Attempt at a Solution

y = (cos 2x)³

u = cos 2x
y = u³

dy/du = -2sin2x
du/dy = 3u²

dy/dx = dy/du * du/dx

dy/dx = -2sin2x * 3(cos² 2x)

= -6sin2x cos²2x

Hi, I've been racking my brain over this question for sometime now, I've attempted it multiple times getting it wrong over and over again. I've got this answer, but, I'm really not confident that it is right. Can you guys take a look at it and work some magic? It's function of a function, which I think is more commonly known as the Chain rule.

Thank you.

 

[Matterwave]

That looks right to me.

 

[Mike2793]

Seriously?

I'm speechless!

 

[skiller]

dy/du = -2sin2x
du/dy = 3u²

should read as:
$$\frac{dy}{du} = 3u^2$$ and
$$\frac{du}{dx} = -2\sin 2x$$
but other than that, it looks fine.

 

[Mike2793]

Haha, there's my attention to detail. Thanks very much, guys, I can finally lay this to rest.