# Trying to differentiate using function of a function/Chain rule

1. Jun 24, 2014

### Mike2793

1. The problem statement, all variables and given/known data

Using the function of a function formula differentiate the following:

y = (cos 2x)3

2. Relevant equations

dy/dx = dy/du * du/dx

3. 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.

2. Jun 24, 2014

### Matterwave

That looks right to me.

3. Jun 24, 2014

### Mike2793

Seriously?

I'm speechless!

4. Jun 24, 2014

### skiller

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

5. Jun 25, 2014

### Mike2793

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