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

Kummer

I answered your question in your other post.

5. Aug 8, 2007

Dick

That's the second time you done this today (at least). The idea of the Homework Forum is NOT to post complete solutions. The idea is to HELP the poster to solve the problem themselves by giving them guidance. Not to do the work for them. With alll due respect, you've been around for a while, hasn't anyone pointed this out to you before?

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