ANOTHER EXAMPLE

dxn/dx = limh --> 0 [(x + h)n - xn]/h =

limh --> 0 [xn(1 + h/x)n - xn]/h =

use binomial theorem

limh --> 0 xn(1 + nh/x +(n2)h2/x2 +…+hn/ xn]/h =

limh --> 0 [xn + nhxn-1 +(n2)h2xn-2 +…+hn -xn]/h=

nxn-1

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