Unformatted text preview: f ( x ) = x n . Here n is a number of any kind: integer, rational, positive, negative, even irrational, as in x π . We have already computed some simple examples, so the formula should not be a complete surprise: d dx x n = nx n1 . It is not easy to show this is true for any n . We will do some of the easier cases now, and discuss the rest later. The easiest, and most common, is the case that n is a positive integer. To compute the derivative we need to compute the following limit: d dx x n = lim Δ x → ( x + Δ x ) nx n Δ x . 45...
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 Spring '07
 JonathanRogawski
 Math, Calculus, Derivative, Finding Derivatives, small collection

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