What does it mean to differentiate a function?

Differentiate means take a derivative. You will need to know the rules for derivatives, unless you decide to use the long limit definition... but that's harder to prove for trig functions.

Important rule(s) for this problem:

##d/dx [sin(u)] = cos(u) * du/dx##

Let ##u = x - 5rArrdu/dx = 1##

##d/dx [sin(x - 5)] = cos(x - 5) * 1 = cos(x - 5)##.