Answer
$$y'=\frac{1}{2\sqrt{x+\sqrt x}}(1+\frac{1}{2\sqrt x})$$
Work Step by Step
$$y'=(\sqrt{x+\sqrt x})'=\frac{1}{2\sqrt{x+\sqrt x}}(x+\sqrt x)'=
\frac{1}{2\sqrt{x+\sqrt x}}(1+\frac{1}{2\sqrt x})$$
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