(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

x^6 + y^6 = -6

I have to prove that y'' = 30x^4/y^11

2. Relevant equations

3. The attempt at a solution

Using implicit differentiation:

6x^5 + 6y^5 dy/dx = 0

6y^5 dy/dx = -6x^5

dy/dx = -x^5/y^5

Quotient Rule:

[(y^5)(-5x^4) - (-x^5)(5y^4 dy/dx)] / (y^5)^2

[-5x^4 y^5 + (x^5) 5y^4 dy/dx] / (y^5)^2

This is where I got stuck.

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# Second derivative using implicit differentiation

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