Answer
$f'(x)=\frac{\sec^2 {h}{\sqrt{x}}}{2\sqrt{x}}$
Work Step by Step
$f'(x)=\frac{d}{dx}\tanh {\sqrt{x}}$
Using the chain rule:
$f'(x)=\frac{d\tanh{\sqrt{x}}}{d(\sqrt{x})}
\times\frac{d(\sqrt{x})}{dx}$
$\DeclareMathOperator{\sech}{sech}$
$=(\sech)^2 {\sqrt{x}}
\times\frac{1}{2\sqrt{x}}$
$=\frac{(\sech)^2{\sqrt{x}}}{2\sqrt{x}}$
