Answer: Sin x
Explanation:
The derivatives for the sin and cos functions are interconnected as follows:
d/dx sin(x) = cos(x)
d/dx cos(x) = -sin(x)
d/dx -sin(x) = - cos(x)
d/dx - cos(x) = sin(x)
(Also worth noting is that cos (-x) = cos(x) and sin(-x) = -sin(x), though those will not have bearing here).
With this in mind, taking the derivative of f(x) = 1-cos(x) would proceed as follows:
d/dx (1 - cos(x)) = d/dx (1) + d/dx (-cos(x)) (Recalling that the derivative of a sum/difference is equal to the sum/difference of the derivatives)
= 0 + sin (x) (recalling that the derivative of a constant is 0)
= sin(x)
