Thread: Formal derivative
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Old November 13th, 2008, 08:42 AM
Laurent Laurent is offline
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Originally Posted by tttcomrader View Post
For a polynomial f(x) reduce \frac {(f(x)-f(z)}{x-z}, substitute Z in for X. Show that this is f'(x).

From calculus I know that as the lim x approaches z that is the derivative, but if I just substitute, how would I compute that? Thanks.
By linearity, you just need to study the case of f(X)=X^k, i.e. to consider \frac{X^k-z^k}{X-z}. This is given by the usual formula: \frac{X^k-z^k}{X-z}=X^{k-1}+zX^{k-2}+\cdots+z^{k-2}X+z^{k-1}. And now, substitute.
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