Answer
$ \frac {-2s^2}{\sqrt{1-s^2}}$
Work Step by Step
Given that $y$ = $s\sqrt{{1-s^2}}+cos^{-1}{s}$, on applying the product rule of the derivative, we get:
$\frac{dy}{ds}$ = ${\sqrt{1-s^2}\frac{ds}{ds}\times{s\frac{d{\sqrt{{1-s^2}}}}{ds}}\times-\frac{1}{\sqrt{1-s^2}}}$
or $\frac{dy}{ds}$ = $\sqrt{1-s^2} \times { \frac {-2s^2}{2\sqrt{1-s^2}}\times-\frac{1}{\sqrt{1-s^2}}}$
oso $\frac{dy}{ds}$ = $\frac{1-s^2}{\sqrt{1-s^2}} \times { \frac {-s^2}{\sqrt{1-s^2}}\times-\frac{1}{\sqrt{1-s^2}}}$
The final answer is: = $ \frac {-2s^2}{\sqrt{1-s^2}}$
