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:
“The biggest difference between ancient Rome and the USA is that in Rome the common man was treated like a dog. In America he sets the tone. This is the first country where the common man could stand erect.”
—I.F. (Isidor Feinstein)
“There are strange flowers of reason to match each error of the senses.”
—Louis Aragon (1897–1982)