If `sqrt(y+x)+sqrt(y-x)=c` ,show that` (dy)/(dx)=y/x-sqrt((y^2)/(x^2)-1.)`

Explanation

We have,



`sqrt{y+x}+sqrt{y-x}=c`



On differentiating w.r.t `x`, we get


`frac{1}{2 sqrt{y+x}}(1+frac{d y}{d x})+frac{1}{2 sqrt{y-x}}(frac{d y}{d x}-1)=0`


`frac{d y}{d x}[frac{1}{sqrt{y+x}}+frac{1}{sqrt{y-x}}]=frac{1}{sqrt{y-x}}-frac{1}{sqrt{y+x}}`


`frac{d y}{d x}=frac{sqrt{y+x}-sqrt{y-x}}{sqrt{y+x}+sqrt{y-x}}=frac{1-sqrt{frac{y-x}{y+x}}}{1+sqrt{frac{y-x}{y+x}}}`


...