Differentiate the second time. Then, sub in y' from the first derivative.
Here is an example:
\(\displaystyle x^{2}+y^{2}=1\)
\(\displaystyle 2x+2yy'=0\)
\(\displaystyle y'=\frac{-x}{y}\)
Now, differentiate \(\displaystyle \frac{-x}{y}\) using the quotient rule.
\(\displaystyle y''=\frac{y(-1)-(-x)y'}{y^{2}}\)
Resub y' from the first time around:
\(\displaystyle y''=\frac{-y-(-x)(\overbrace{\frac{-x}{y}}^{\text{y'}})}{y^{2}}\)
\(\displaystyle y''=\frac{-x^{2}}{y^{3}}-\frac{1}{y}\)
Apply this to your problem.
