How do you find the derivative of ##sin2x - cos2x##?

2cos2x + 2sin2x

differentiate using##color(blue)" chain rule " ##

##d/dx [ f(g(x)) ] = f'(g(x)). g'(x)##

apply this rule to each term

##d/dx(sin2x) = cos2x d/dx(2x) = 2cos2x ##

##d/dx(cos2x) = -sin2x d/dx(2x) = -2sin2x ##

##rArrd/dx(sin2x-cos2x) = 2cos2x + 2sin2x##