The derivative of the function f(x) = sinx⋅(1−cosx) is f'(x) = cosx⋅sinx + sinx⋅(−sinx) = cosx⋅sinx - sin^2(x).
Therefore, the correct answer is f'(x) = cosx⋅sinx - sin^2(x).
Which of the following is the derivative of the function f(x)=sinx⋅(1−cosx) ? (1 point) Responses f′(x)=cosx⋅sinx f ' x = cos x · sin x f′(x)=−cosx⋅sinx f ' x = - cos x · sin x f′(x)=cosx+cosx⋅sinx f ' x = cos x + cos x · sin x f′(x)=cosx−cos2x−sin2x f ' x = cos x - cos 2 x - sin 2 x f′(x)=cosx−cos2x+sin2x
1 answer