Antiderivative means integrating the given function. So, the antiderivative of would be
If you take the derivative of with respect to x, you will get what you integrated, that is,
Likewise, the derivative of , and the antiderivative of
Your answer to find the antiderivative of 3sinx is correct! If what you have asked for (that is finding the antiderivative) is correct, may be your booklet has serious flaws!