Question

How do you differentiate `g(x) = [1 + sin(2x)]*[1 - sin(2x)]` using the product rule?

Answer 1

We notice that

#g(x)=[1+sin2x]*[1-sin2x]=>g(x)=1-sin^2(2x)=> g(x)=cos^2(2x)#

Hence the derivative is

#g'(x)=2*cos(2x)(-sin2x*2)=> g'(x)=-4sin2xcos2x#