A Common Error
It is a common error, when studying calculus, to suppose that the derivative of (uv) equals (u ′)(v ′). Leibniz himself made this error initially; however, there are clear counterexamples. Consider a differentiable function ƒ(x) whose derivative is ƒ '(x). This function can also be written as ƒ(x) · 1, since 1 is the identity element for multiplication. If the above-mentioned misconception were true, (u′)(v′) would equal zero. This is true because the derivative of a constant (such as 1) is zero and the product of ƒ '(x) · 0 is also zero.
Read more about this topic: Product Rule
Famous quotes containing the words common and/or error:
“England still waits for the supreme moment of her literature—for the great poet who shall voice her, or, better still, for the thousand little poets whose voices shall pass into our common talk.”
—E.M. (Edward Morgan)
“It is an error to believe that the Roman Pontiff can and ought to reconcile himself to, and agree with, progress, liberalism, and contemporary civilization.”
—Pope Pius IX (1792–1878)