If `ysqrt(1-x^2)+xsqrt(1-y^2)=1` show that `(dy)/(dx)=-sqrt((1-y^2)/(1-x^2))`

Explanation

$$ x \sqrt{1-y^{2}}+y \sqrt{1-x^{2}}=1 $$
Differentiating throughout with respect to `x` we get
$$
\begin{aligned}
&x \frac{1}{2 \sqrt{1-y^{2}}} \cdot(-2 y) \frac{d y}{d x}+\sqrt{1-y^{2}}+y \frac{1}{2 \sqrt{1-x^{2}}} \cdot(-2 x)+\sqrt{1-x^{2}} \frac{d y}{d x}=0 \\
&\Rightarrow \frac{-x y}{\sqrt{1-y^{2}}} \frac{d y}{d x}+\sqrt{1-y^{2}}+\frac{(-x y)}{\sqrt{1-x^{2}}}+\sqrt{1-x^{2}} \frac{d y}{d x}=0 \\
...