Derivative of $\arctan \sqrt x$

Question

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}?

These coincide where they are both defined. – Did Mar 22 '13 at 15:15 — Did, Mar 22 '13 at 15:15

score 6 · Accepted Answer · answered Mar 22 '13 at 15:15

6

For $\sqrt{x}$ to be defined, we need $x\geq 0$. So $x = \lvert x \rvert$, and both terms are the same.

answered Mar 22 '13 at 15:15

Stefan

1 Answers1