Answer:
A)

Explanation:
Use implicit differentiation to find dy/dx

Determine d²y/dx² using dy/dx
![(dy)/(dx)=(-y)/(x)\\ \\ (d^2y)/(dx^2)=((x)[(d)/(dx)(-y)]-(-y)[(d)/(dx)(x)] )/(x^2)\\ \\ (d^2y)/(dx^2)=(-x(dy)/(dx)+y)/(x^2)\\ \\ (d^2y)/(dx^2)=(-x((-y)/(x))+y)/(x^2)\\\\ (d^2y)/(dx^2)=(-(-y)+y)/(x^2)\\\\ (d^2y)/(dx^2)=(y+y)/(x^2)\\\\ (d^2y)/(dx^2)=(2y)/(x^2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/n8ge9yogtvhrpd06izyw0q4h1dysba7ss4.png)
Helpful tips
- When doing implicit differentiation, make sure to treat "y" as a constant and write dy/dx next to the y-term because it's differentiated with respect to x
- The product rule is
![(d)/(dx)[f(x)g(x)]=f(x)[(d)/(dx)g(x)]+[(d)/(dx)f(x)]g(x)](https://img.qammunity.org/2023/formulas/mathematics/high-school/re9nqd81uf1oujimlz4ysk3oyloucv55pz.png)
- The quotient rule is
![(d)/(dx)[(f(x))/(g(x))]=(f(x)[(d)/(dx)g(x)]-g(x)[(d)/(dx)f(x)])/((g(x))^2)](https://img.qammunity.org/2023/formulas/mathematics/high-school/34s0jtp2s2r28qwxcauijq7531950uvinv.png)
represents the first derivative of y with respect to x and
represents the second derivative of y with respect to x
Let me know if you have any more questions!