I was thinking how do I differentiate the domain of functions...(adsbygoogle = window.adsbygoogle || []).push({});

Suppose I have a function:

[tex]f(x) = \left\{\begin{matrix}

x^2 -1, \;\; |x| \leq 1\\

1 - x^2, \;\; |x| > 1

\end{matrix}\right.[/tex]

And I need to derive it:

[tex]f'(x) = \left\{\begin{matrix}

2x, \;\; |x| \leq 1\\

-2x, \;\; |x| > 1

\end{matrix}\right.[/tex]

1. What do I do with the conditions of |x| ? Is there a rule to handle this?

2. What will be the domain of f'(x)? Will the domain of f'(x) be the domain of f(x) minus the points where the function is non-differentiable?

Thank you,

Rafael Andreatta

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# Question about domain of derivatives

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