How would you find the second derivative of an implicit function?

y^2-x^2=16

Heres my attempt:

2y(dy/dx)-2x=0

2y(dy/dx)=2x

2y(dy/dx)/2y=2x/2y

dy/dx= x/y

This is only the first derivative. I think I'm suppose to plug in dy/dx back into the original equation. Am I on the right track?

y^2-x^2=16

Heres my attempt:

2y(dy/dx)-2x=0

2y(dy/dx)=2x

2y(dy/dx)/2y=2x/2y

dy/dx= x/y

This is only the first derivative. I think I'm suppose to plug in dy/dx back into the original equation. Am I on the right track?

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