Derivative of f(x) = 2 cos(x) + sin(2x)?

Question

f(x) = 2 cos(x) + sin(2x)

Answer 1

f(x) = 2cosx+sin(2x)

f(x) = 2cosx+2sinxcosx

Apply derivative to each side with respect of x.

d/dx(f(x)) = d/dx(2cosx+2sinxcosx)

= d/dx(2cosx)+d/dx(2sinxcosx)

= -2sinx+2cosx(cosx)-2sinx(sinx)

= -2sinx+2cos^2x-2sin^2x

= -2sinx+2(cos^2x-sin^2x)

= -2sinx+2cos2x

= 2cos(2x)-2sinx