Test-55.pdf - In other words for every r ∈ Q,
(fr)′(c...

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In other words, for every r Q, (f r ) (c) = rf(c) r 1 f (c), provided f(c) > 0 if r ̸ Z and f(c) ̸ = 0 if r Z with r < 0. Example 4.8. As a particular case of the results in Remark 4.7 and Exam- ples 4.1 (i), (ii), we see that the nth power function is differentiable on R for each nonnegative integer n, and d (x n ) = nx n 1 . dx
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Moreover, the above result is valid for negative integral powers, provided x ̸ = 0, and for rational nonintegral powers, provided x > 0.
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  • Spring '14
  • ThomasW.Appelquist
  • Derivative, above result

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