(a) State the rule used to obtain the derivative of the product of two differentiable functions.
(b) Let f(x)=x2+1 and g(x)=x−3. Find (fg)′(x) by directly applying the rule stated in part (a).
(c) Expand (fg)(x) first, then differentiate the expanded expression term-by-term and show that your answer agrees with the result from part (b).
(d) Explain briefly why both methods give the same derivative, even though the algebraic steps look different.