# Simple Differential problem

1. Aug 8, 2007

### John O' Meara

Given that $$\frac{dx}{dy} = (\frac{dy}{dx})^{-1}\\$$, differentiate throughout with respect to x and show that $$\frac{d^2x}{dy^2} = \frac{- \frac{d^2y}{dx^2}}{(\frac{dy}{dx})^3}\\$$.

An attempt: $$\frac{d^2 x}{dx dy} = \frac{d (\frac{dy}{dx})^{-1}}{dx} \\$$.

I need help to get me started. Thanks for the help.

Last edited: Aug 8, 2007
2. Aug 8, 2007

### John O' Meara

Sorry for the second post. It wasn't meant to happen.

3. Aug 8, 2007

### matness

It is better to start with $$\frac{d^2x}{dy^2} = \frac{d}{dy}\big(\frac {dx}{dy})$$

Last edited: Aug 8, 2007
4. Aug 8, 2007