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y=sqrt(x+y)" to prove that "(dy)/(x)=...

y=sqrt(x+y)" to prove that "(dy)/(x)=

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If sqrt(x) + sqrt(y) = sqrt(a) , prove that (dy)/(dx) = -sqrt(y/x) .

If y=sqrt(x/a)+sqrt(a/x) , prove that 2x y(dy)/(dx)=(x/a-a/x)

If x sqrt(1+y)+y sqrt(1+x)=0, prove that (dy)/(dx)=-(1)/((x+1)^(2))

If sqrt(x) + sqrt(y) = sqrt(5) , Prove that (dy)/(dx) = (-3)/(2) when x= 4" and "y=9 .

If y=sqrt(x)+1/(sqrt(x)) , prove that 2x(dy)/(dx)=sqrt(x)-1/(sqrt(x))

If y = sqrt(x) + (1)/(sqrt(x)) prove that 2x(dy)/(dx) + y = 2sqrt(x)

If x sqrt(1+y)+y sqrt(1+x)=0, then prove that (dy)/(dx)=-(1+x)^(-2)

If x sqrt ( 1+ y) + y sqrt( 1+x) =0 , prove that (dy)/( dx) = - (1)/( (1+x)^2) .

If y= sqrt ( x) + (1)/( sqrtx ) , prove that 2x (dy)/( dx ) + y=2 sqrt (x ) .

If y=sqrt(x)+(1)/(sqrt(x)), prove that 2x(dy)/(dx)=sqrt(x)-(1)/(sqrt(x))