Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of (x)g(x) was (x)g(x),

Gottfried Leibniz, one of the inventors of calculus, initially thought that the derivative of ƒ(x)g(x) was ƒ′(x)g′(x), based on the example ƒ(x) = x² + bx and g(x) = cx + d. Besides neglecting to work out the details, which would have shown his error, he made an erroneous conclusion based on one example, rather than a mathematical proof.

(a) Calculate ƒ′(x)g′(x).
(b) Calculate [ƒ(x)g(x)]; and verify that your answer is different than your answer to part (a).