What rules can be used to find the 4th derivative of cos(2x)?

[Cacophony]

Homework Statement

see title.

Homework Equations

no

The Attempt at a Solution

Ok so the solution is 16cos(2x) but I'm not sure how it is derived to that. I've tried the product rule but it's not working for me. What rule or rules do I use to get this solution?

 

[mtayab1994]

Well if you calculate the first derivative properly you should be yielded to -2sin(2x).
Edit: Take into consideration that the derivative of cos(Ux)= -u'(x)*sin(x)

 

[Cacophony]

Ok cool but what rule did you use there?

 

[micromass]

The chain rule.

 

[HallsofIvy]

You don't need the product rule because do not have a product of two functions of x. You need the chain rule because you have f(y)= 2cos(y) and y= 2x:
$$\frac{df}{dx}= \frac{df}{dy}\frac{dy}{dx}$$
With f(y)= cos(y), what is df/dy? With y= 2x, what is dy/dx?

 

[Mark44]

You don't need the product rule because do not have a product of two functions of x. You need the chain rule because you have f(y)= 2cos(y) and y= 2x:

Make that f(y)= cos(y)

$$\frac{df}{dx}= \frac{df}{dy}\frac{dy}{dx}$$
With f(y)= cos(y), what is df/dy? With y= 2x, what is dy/dx?

 

[HallsofIvy]

Make that f(y)= cos(y)

Right. Thanks for the correction.