# Homework Help: 4th derivative of cos(2x)

1. Apr 10, 2012

### Cacophony

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

see title.

2. Relevant equations
no

3. 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?

2. Apr 10, 2012

### 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)

3. Apr 12, 2012

### Cacophony

Ok cool but what rule did you use there?

4. Apr 12, 2012

### micromass

The chain rule.

5. Apr 12, 2012

### 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?

6. Apr 12, 2012

### Staff: Mentor

Make that f(y)= cos(y)

7. Apr 12, 2012

### HallsofIvy

Right. Thanks for the correction.