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## Homework Statement

Find y''(x) of the parametric equation 9x^2+y^2=9 using implicit differentiation.

## Homework Equations

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)

=-9(d/dx)(xy^-1)

=-9(x(d/dx)(y^-1)+(y^-1)(dx/dx))

=-9(-x(y^-2)y'(x)+y^-1)

I substituted the value of y'(x) = -9x/y here

=-9((-x/(y^2))(-9x/y)+(1/y))

=-9((9x^2)/(y^3)+(1/y))

=(-81x^2)/(y^3)-(9/y)

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.