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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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    $\begingroup$ These coincide where they are both defined. $\endgroup$
    – Did
    Mar 22, 2013 at 15:15

1 Answer 1

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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.

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