Would there ever be marks for differentiating by hand on an Exam 2 - given that the question didn't specifically ask you to 'show' or w/e?
Very possibly, they can ask you to use calculus, which means you only need to show yourself applying the power/chain/product/quotient rule, or worse, they can ask you to use algebra, which means ALL the working of the question must be done by hand, including calculus. They very rarely do latter, but its possible.
If they haven't asked you to use calculus, but its a 3 or more mark question involving differentiation (not necessarily asking for the derivative), use your best judgement. If there are 4 critical steps to the question and 3 marks, that may indicate stating the derivative is not important and simply saying "let f'(x) = 0"... etc may be sufficient. Otherwise, state the derivative.
Of course show that's are similar in that you can't take any shortcuts but you are allowed to use CAS for non-important steps, like evaluation of an integral with its terminals after you've stated it in square bracket terminal form.