Okay, so I know how to get derivatives, but I have spent the last hour trying to figure this out and this is really frustrating me

. Help please. I don't understand how to get the answers to these two problems. I have the answers but the idea is to understand them which i don't.

f(x) = sin x, - pi/2 is less than or equal to x which is less than or equal to, pi/2 with the real number 1/2

f(x) = x^3 - (4/x) with the real number of 6

my professor did a bad job of explaining how to do these problems please help. I'm studying for an exam right now and this is all that seems to be stumping me