# Differentiability of composite functions

Hi, I have a small question about this. Using the chain rule, I know that a composition of differentiable functions is differentiable. But is it also true that if a composition of functions is differentiable, then all the functions in the composition must be differentiable?

For example, if $f(g(x))$ is differentiable, does that imply $f(x)$ and $g(x)$ are both differentiable?

Thanks!

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Hi, I have a small question about this. Using the chain rule, I know that a composition of differentiable functions is differentiable. But is it also true that if a composition of functions is differentiable, then all the functions in the composition must be differentiable?

For example, if $f(g(x))$ is differentiable, does that imply $f(x)$ and $g(x)$ are both differentiable?

Thanks!

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

DonAntonio

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