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If ysqrt(1-x^2)+xsqrt(1-y^2)=1,"p r o v...

If `ysqrt(1-x^2)+xsqrt(1-y^2)=1,"p r o v et h a t"(dy)/(dx)=sqrt((1-y^2)/(1-x^2))dot`

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Given`ysqrt(1-x^2)+xsqrt(1-y^2)=1`
Differentiating throughout with respect to x we get
=`(x1)/(2(sqrt(1−y^2))) ​(−2y)(dy/dx)​+sqrt(1−y^2) ​+y/(2sqrt(1−x^2)) ​​⋅(−2x)+sqrt(1−x^2) ​(dy/dx)​=0`
=`(-xy)/(sqrt(1−y^2))(dy/dx)+sqrt(1−y^2)+(-xy)/(2sqrt(1−x^2))+sqrt(1−x^2) ...
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