Trouble finding second implicit derivative I have trouble finding the second implicit derivative.
This is the question.
Find y'' in terms of x and y by implicit differentiation.
$x^5 +y^5 = 2^5$
The final answer I always get is $\displaystyle -\frac{(4x^3)(32)}{y^9}$.
I might be doing something wrong

Take the derivative with respect to x, use y' and y'' to denote the first and second derivative of y with respect to x. 
$\displaystyle 5x^4+5y^4y'=0$
Take the derivative again 
$\displaystyle 20x^3+5(4y^3y'(y')+y^4y'')=0$ 
Rearrange to get, 
$\displaystyle y''=\frac{-20x^3-20y^3(y')^2}{y^4}=\frac{-20x^3-20y^3(-x^4/y^4)^2}{y^4}$
