# How do you differentiate #f(x) = sin(2x)cos(2x)# using the product rule?

##### 1 Answer

#### Answer:

See the explanation section below.

#### Explanation:

Differentiate

**using the product rule**

I use the order: the derivative of a product of functions is the derivative of the first times the second, plus: the first times the derivative of the second.

Note that we shall need the chain rule for the derivatives of

You may choose to write

# = 2cos^2(2x)-2sin^2(2x)#

Your teacher/textbook may well prefer to rewrite this answer using

# = 2[cos^2(2x)-sin^2(2x)]#

# = 2cos(4x)#

Although if you're going to do that, I suggest

**Rewriting the function**

Use

Now we do not need the product rule, only the chain rule (which we needed in the other method also).