`(d^2x)/(dy^2)` equals:
`(1.) ` `((d^2y)/(dx^2))^-1`
`(2)` `-((d^2y)/(dx^2)) ((dy)/(dx))^-3`
`(3)` `-((d^2y)/(dx^2))^-1 ((dy)/(dx))^-2`
`(4)` `-((d^2y)/(dx^2))^-1 ((dy)/(dx))^3`

Explanation

To solve the problem of finding \(\frac{d^2x}{dy^2}\) in terms of \(\frac{d^2y}{dx^2}\) and \(\frac{dy}{dx}\), we can use the chain rule and the relationship between derivatives. Let's go through the steps:

### Step 1: Understand the relationship between \(x\) and \(y\)
We know that \(x\) is a function of \(y\) and \(y\) is a function of \(x\). Therefore, we can express the derivatives accordingly.

### Step 2: Find the first derivative \(\frac{dx}{dy}\)
Using the chain rule, we have:
\[
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