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

First, $\displaystyle x^5+y^5=2^5 \rightarrow 5x^4+5y^4\cdot{y'}=0 \Rightarrow y'=-\frac{x^4}{y^4}$.
Second, $\displaystyle 5x^4+5y^4\cdot{y'}=0 \rightarrow 20x^3+20y^3\cdot{y'}+5y^4\cdot{y''}=0 \Rightarrow y''=-\frac{4x^3+4y^3\cdot{y'}}{y^4}$.
Using $\displaystyle y'=-\frac{x^4}{y^4}$ we will get $\displaystyle y''=-\frac{4x^3+4y^3\cdot{(-\frac{x^4}{y^4})}}{y^4}=-\frac{4x^3-\frac{4x^4}{y}}{y^4}=\frac{4x^3(x-y)}{y^5}$.
