Implicit Differentiation of the second derivative.

[jdx10n]

I am able to find dy/dx, but when it comes to plugging in dy/dx and simplifying, I am completely lost.
Here is the problem...

x^3+y^3=1

 

[galactus]

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.