Question

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

• A. $\frac{2}{c}$
• B. $-\frac{2}{c^2}$
• C. $\frac{2}{c^2}$
• D. $-\frac{2}{c}$

Answer 1

The correct option is C $\frac{2}{c^2}$

$\sqrt{x+y}=c-\sqrt{y-x}$
On squaring we get,
$2x-c^2=-2c\sqrt{y-x}$
Again squaring we get,
$y=\frac{(2x-c^2{)}^2}{4c^2}+x$
$y^{\prime }=\frac{4(2x-c^2)}{4c^2}+1$
$y^{\prime \prime }=\frac{8}{4c^2}=\frac{2}{c^2}$
Option C