a)find the differential dy of the function y(x)=x√(1-x^2)
defined for x in (-1,1)
B) for the function y(x)=x√(1-x^2) use the result in a) to find dy when x=0.0 and dx=0.01. Compare the value with delta y for x=0.0 and dx=0.01
Assuming that you meant you want to find the derivative
$\displaystyle \displaystyle \begin{align*} y &= x\sqrt{1-x^2} \\ y^2 &= x^2(1 - x^2) \\ y^2 &= x^2 - x^4 \\ \frac{d}{dx}\left(y^2\right) &= \frac{d}{dx}\left(x^2 - x^4\right) \\ 2y\,\frac{dy}{dx} &= 2x - 4x^3 \\ \frac{dy}{dx} &= \frac{2x - 4x^3}{2y} \\ \frac{dy}{dx} &= \frac{x - 2x^3}{y} \\ \frac{dy}{dx} &= \frac{x - 2x^3}{x\sqrt{1 - x^2}} \\ \frac{dy}{dx} &= \frac{1 - 2x^2}{\sqrt{1 - x^2}} \end{align*}$