If x+y−x−y=c , then d2ydx2=

x+y−x−y=cS.o.b.s and simplifying 4y2=4xc2−c4 8ydydx=4c2⇒2(dydx)2+2yd2ydx2=0 ⇒d2ydx2=−(dydx)2y=−c44y3

If x+y−x−y=c , then d2ydx2=

x+y−x−y=cS.o.b.s and simplifying 4y2=4xc2−c4 8ydydx=4c2⇒2(dydx)2+2yd2ydx2=0 ⇒d2ydx2=−(dydx)2y=−c44y3

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If $\sqrt{x + y} - \sqrt{x - y} = c$ , then $\frac{d^{2} y}{d x^{2}} =$

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$\frac{1}{y} {(\frac{d y}{d x})}^{2}$

$\frac{- c^{4}}{4 y^{3}}$

$y {(\frac{d y}{d x})}^{2}$

$\frac{- c^{2}}{4 y^{3}}$

answer is B.

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Detailed Solution

$\sqrt{x + y} - \sqrt{x - y} = c$
S.o.b.s and simplifying
$4 y^{2} = 4 x c^{2} - c^{4} 8 y \frac{d y}{d x} = 4 c^{2} \Rightarrow 2 {(\frac{d y}{d x})}^{2} + 2 y \frac{d^{2} y}{d x^{2}} = 0 \Rightarrow \frac{d^{2} y}{d x^{2}} = - \frac{{(\frac{d y}{d x})}^{2}}{y} = \frac{- c^{4}}{4 y^{3}}$