Remove arbitrary constants from the function $x = c_1 \cos wt + c_2 \sin wt$, where $c_1, c_2$ are arbitrary constants.

Question

From the user:

Please help me. I've been trying to do and I can't resolve, because I'm confusing I don't know if  derive dt/dw or dw/dt. I know that I have to derive implicitly.

Thanks.

Note: Clay6 has edited the question for clarity.