The derivative of $\arctan \sqrt x$ is
\begin{equation} \frac{1}{2\sqrt x(1+x)} \end{equation}
or
\begin{equation} \frac{1}{2\sqrt x(1+|x|)} \end{equation}?
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4$\begingroup$ These coincide where they are both defined. $\endgroup$– DidMar 22, 2013 at 15:15
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1 Answer
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For $\sqrt{x}$ to be defined, we need $x\geq 0$. So $x = \lvert x \rvert$, and both terms are the same.
