Differentiating \frac{dx}{dy} = (\frac{dy}{dx})^{-1} with Respect to x

[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.

 

[John O' Meara]

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

 

[matness]

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

 

[Kummer]

I answered your question in your other post.

 

[Dick]

I answered your question in your other post.

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?