Find y''(x) of the parametric equation 9x^2+y^2=9 using implicit differentiation.
I already came up with y'(x) = -9x/y
The Attempt at a Solution
Here is what I have for y''(x) so far
y''(x) = d/dx (-9xy^-1)
I substituted the value of y'(x) = -9x/y here
I know this is incorrect, I originally tried this using the quotient rule but was getting the same answer and the work was much more jumbled, so I opted for the product rule.
The book states the answer is -81/(y^3). I am stuck and haven't been able to work towards the right answer.