How do you differentiate #f(x)= sin2xcos2x# using the product rule?
1 Answer
Jul 19, 2017
# f'(x) = 2cos4x #
Explanation:
Using the trig identity:
# sin2A -= 2sinAcosA #
We have:
# sin4A -= 2sin2Acos2A #
So we can write:
# f(x) = sin2xcos2 #
# " " = 1/2sin4x #
And so, using the chain rule we have:
# f'(x) = 1/2cos4x * 4#
# " " = 2cos4x #
This is an easier method than using the product rule