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

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

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

if y=sqrt(x^(2)+a^(2)), then show that y(dy)/(dx)=x

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

If y={x+sqrt(x^(2)+a^(2))}^(n), then prove that (dy)/(dx)=(ny)/(sqrt((x^(2)+a^(2))))

If y={x+sqrt(x^(2)+a^(2))}^(n), then prove that (dy)/(dx)=(ny)/(sqrt(x^(2)+a^(2)))

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

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

If y=log{x+sqrt(x^(2)+a^(2))}, prove that: (x^(2)+a^(2))(d^(2)y)/(dx^(2))+x(dy)/(dx)=0

If tan^(-1)(Y/X) = log (sqrt(X^2+Y^2)) , prove that (dy/dx) = ((X+Y)/(X-Y))