How I can calculate the derivative of $$f(x) = \left\{ \begin{gathered} {x^2}\quad,\quad{\text{if}}\quad x \in \mathbb{Q} \\ {x^3}\quad,\quad{\text{if}}\quad x \notin \mathbb{Q} \\ \end{gathered} \right.$$ at some $x\in \mathbb{R}$?
How I can calculate the derivative of a piecewise function like this?
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calculus
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1There are actually _two_ points where this function is continuous: the two points where the graphs of the cubic and quadratic functions intersect. But it's differentiable at only one of them. – 2011-08-11
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0Exactly. I've seen it. – 2011-08-12