what is the derivative of:

Question

y=2sinxcosx

Answer 1

to ways to do it

1. recognize that 2sinxcosx = sin(2x)
then dy/dx = 2cos(2x)

or

2. y = 2sinxcosx
dy/dx = 2sinx(-sinx) + 2cosx(cosx)
= 2(cos^2x - sin^2x)
which just happens to be 2cos(2x) as above