√x+√y=√a
Find second derivative at x=a
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√x+√y=√a
or √y=√a-√x
1/2√x.dy/dx =-1/√x
dy/dx=-√y/√x
dy/dx=-(√a-√x)/√x
d^2y/dx^2=-{√x(0-1/2√x)-1/2√x(√a-√x)}/(√x)^2
=-{-1/2-1/2√x(√a-√x)}/x
=-1/2+1/2√x(√a-√x)/x
=1/2{1+(√a-√x)/√x}/x
=1/2(√x+√a-√x)/x√x
=√a/2x√x this is your answer
or √y=√a-√x
1/2√x.dy/dx =-1/√x
dy/dx=-√y/√x
dy/dx=-(√a-√x)/√x
d^2y/dx^2=-{√x(0-1/2√x)-1/2√x(√a-√x)}/(√x)^2
=-{-1/2-1/2√x(√a-√x)}/x
=-1/2+1/2√x(√a-√x)/x
=1/2{1+(√a-√x)/√x}/x
=1/2(√x+√a-√x)/x√x
=√a/2x√x this is your answer
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