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

Question

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

Answer 1

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

dy/dx = -2sinx + 2cos(2x)

This is because the derivative of cos(x) is -sin(x)

and the derivative of cos(2x) is (2 x sin(2x))

Answer 2

d/dx 2 cos(x) + d/dx sin(2x) =

2 * d/dx cos(x) +d/dx sin(2x) * d/dx 2x =

(for sin(2x) take the derivative of sin and multiply by the derivative of the 2x inside)

2 * -sin(x) + cos(2x) *2 =

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

2cos(2x) - 2sin(x)

Answer 3

-2sinx+2cos2x