Are the following sets of functions linearly independent or not? Explain your answer.

a) $\displaystyle f(X):= \sin{(2X)}+e^X,f'(X),f''(X),f'''(X)$.

b) $\displaystyle f(X):=X^3+1,f(X)^2,f(X)^3$

c) $\displaystyle \cos{(2x)},\sin{(X)}^2,\cos{(X)}^2$

Literally no clue here, our teacher for this module is shockingly bad. I would ask you not to be vague in your answers, but I'm asking for help it would be a little rude, but yeah... assume I know little to nothing about this topic