Answer
$ -\displaystyle \frac{x}{\sqrt{1-x^{2}}}$
Work Step by Step
f(x) is a composite function$, f(x)=u(v(x))$, where
$u(x)=\sqrt{x}=x^{1/2},\quad v(x)=1-x^{2}$
Apply the Chain rule: $\displaystyle \frac{df}{dx}=\frac{du}{dv}\frac{dv}{dx}$
$\displaystyle \frac{du}{dv}=\frac{1}{2}v^{-1/2}=\frac{1}{2\sqrt{v}}=\frac{1}{2\sqrt{1-x^{2}}}$
$\displaystyle \frac{dv}{dx}=-2x$
$\displaystyle \frac{df}{dx}=\frac{du}{dv}\frac{dv}{dx}=\frac{1}{2\sqrt{1-x^{2}}}\cdot(-2x)$
$=-\displaystyle \frac{x}{\sqrt{1-x^{2}}}$
