9x^2 +y^2 = 9
18x + 2yy' = 0
2yy' = -18x
y' = -18x/2y = -9x/y
where y'= dy/dx = d/dx depending what notation you use.
y'' = d/dx[ -9x/y]
= -9x * (-1y^-2)*y' + y^-1 *(-9)
= (9xy' / y^2 ) - (9/y)
Then I plug in y'
y'' = (9x * (-9xy^-1) / y^2 ) - (9/y)
y'' = -9* ((9x^2 + y^2)/(y^3)) this is right according to the solution
9x^2+y^2 = 9 from the original equation
But the solution goes on with the next step:
y'' = -9 * (9/y^3) = -81/y^3
And I do not know how they get this last step.
Can someone help with that?