implicit derivative for equation $y^5 = x^8$ I'm having a bit of trouble finding the second implicit derivative for the equation $y^5 = x^8$.
I have the first derivative, which is $8x^7 / 5y^4$, but I'm having trouble after that. I did the quotient rule and got $280x^6y^4 - 160x^7y^3 / (20y^3)^2$. I'm not quite sure what to do after this. Any help would be appreciated. Thanks!

$${ y }^{ 5 }-x^{ 8 }=0\\ \\ 5{ y }^{ 4 }\frac { dy }{ dx } -8{ x }^{ 7 }=0\\ \frac { dy }{ dx } =\frac { 8{ x }^{ 7 } }{ 5{ y }^{ 4 } } \\ \frac { { d }^{ 2 }y }{ d{ x }^{ 2 } } =\frac { d }{ dx } \left( \frac { 8{ x }^{ 7 } }{ 5{ y }^{ 4 } }  \right) =\frac { 56{ x }^{ 6 }\cdot 5{ y }^{ 4 }-8{ x }^{ 7 }\cdot 20{ y }^{ 3 }\frac { dy }{ dx }  }{ { \left( 5{ y }^{ 4 } \right)  }^{ 2 } } =\frac { 280{ x }^{ 6 }{ y }^{ 4 }-160{ x }^{ 7 }{ y }^{ 3 }\frac { 8{ x }^{ 7 } }{ 5{ y }^{ 4 } }  }{ 25{ y }^{ 8 } } \\ =\frac { 280{ x }^{ 6 }{ y }^{ 4 }-256{ x }^{ 14 }{ y }^{ -4 } }{ 25{ y }^{ 8 } } $$
