How do you differentiate #f(x) = sin(2x)cos(2x)# using the product rule?
See the explanation section below.
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
Now we do not need the product rule, only the chain rule (which we needed in the other method also).