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:
“We therefore commit his body to the ground; earth to earth, ashes to ashes, dust to dust; in sure and certain hope of the Resurrection.”
—The Burial Service, Book of Common Prayer (1662)
“What has been the effect of [religious] coercion? To make one half the world fools, and the other half hypocrites. To support roguery and error all over the earth.”
—Thomas Jefferson (1743–1826)