Question 791832
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I'm going to go way out on a limb here and assume that you mean the "difference quotient"


Just like any other difference quotient:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{f(x\ +\ h)\ -\ f(x)}{h}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{(x\ +\ h)^4\ -\ x^4}{h}]


Use the binomial expansion:


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \left(\alpha\ +\ \beta\right)^n\ =\ \sum_{\small{k\,=\,0}}^n\LARGE \,{n \choose k}\,\alpha^{n-k}\beta^k]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{x^4\ +\ 4x^3h\ +\ 6x^2h^2\ +\ 4xh^3\ +\ h^4\ -\ x^4}{h}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ \frac{4x^3h\ +\ 6x^2h^2\ +\ 4xh^3\ +\ h^4}{h}]


*[tex \LARGE \ \ \ \ \ \ \ \ \ \ 4x^3\ +\ 6x^2h\ +\ 4xh^2\ +\ h^3]


John
*[tex \LARGE e^{i\pi}\ +\ 1\ =\ 0]
<font face="Math1" size="+2">Egw to Beta kai to Sigma</font>
My calculator said it, I believe it, that settles it
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