Domain Differentiation question


by Bachelier
Tags: differentiation, domain
Bachelier
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#1
Dec10-12, 07:51 PM
P: 376
if a function f is differentiable of [0,2pi] can I integrate its derivative df on [-pi, pi]?
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Vorde
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#2
Dec10-12, 08:51 PM
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First of all, df is not the derivative of f, it is the differential of f, ##\frac{df}{dx}## is the derivative of x (assuming f is a function of x).

Second of all, why would you think that it's derivative would have a different domain?
HallsofIvy
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#3
Dec11-12, 08:15 PM
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The function, f(x)= 0 if x< 0 and rational or [itex]x> 2\pi[/itex] and rational, f(x)= 1 if x< 0 and irrational or [itex]x> 2\pi[/itex] and irrational, f(x)= 3 for all other x, is differentiable for all x in [itex][0, 2\pi][/itex] but not differentiable for any other f. Since it does not have a derivative on [itex][-\pi, 0][/itex], no, its derivative cannot be integegrated there!


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