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If we let [itex]y = x^r[/itex], then [itex]\ln y = r\ln x[/itex], and then by implicit differentiation

[itex]\frac{y'}{y} = \frac{r}{x},[/itex]

and thus it follows that

[itex]y' = \frac{ry}{x} = \frac{rx^r}{r} = rx^{r-1}.[/itex]

But the statement [itex]\ln y = r\ln x[/itex] also requires [itex]x>0[/itex], so does the General Power Rule only applies to positive real values of

*x*?

Thanks.