- #1

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For example, if [itex]f(g(x))[/itex] is differentiable, does that imply [itex]f(x)[/itex] and [itex]g(x)[/itex] are both differentiable?

Thanks!

- Thread starter raphile
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- #1

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For example, if [itex]f(g(x))[/itex] is differentiable, does that imply [itex]f(x)[/itex] and [itex]g(x)[/itex] are both differentiable?

Thanks!

- #2

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For example, if [itex]f(g(x))[/itex] is differentiable, does that imply [itex]f(x)[/itex] and [itex]g(x)[/itex] are both differentiable?

Thanks!

[itex]\cos\sqrt{x}[/itex] is differentiable from the right at [itex]x=0[/itex] , but [itex]\sqrt{x}[/itex] isn't...

DonAntonio

- #3

Office_Shredder

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A classic example of this is when f(x)=1 and g(x) is any function you pick. f(g(x))=1 so this composition is differentiable, but g(x) clearly doesn't have to be.

For the other way around consider f(x)="any function which is always negative" if x<1 (for example -x

- #4

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Thanks for the help and examples!

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