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For any rational number r give a definition of f(x) = x" for r > 0 and show f'(x) = rx*-1.

For any rational number r give a definition of f(x) = x" for r > 0 and show f'(x) = rx*-1.

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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For any rational number \( r \), give a definition of \( f(x) = x^r \) for \( x > 0 \) and show \( f'(x) = rx^{r-1} \).
Transcribed Image Text:For any rational number \( r \), give a definition of \( f(x) = x^r \) for \( x > 0 \) and show \( f'(x) = rx^{r-1} \).
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