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Help rewriting a differential equation

Hey, hope someone will help me :)

I need some help to rewrite a differential equation.

I start with the expression :

Attachment 22937

This reason why this apply (correct me if I'm wrong) is this:

Attachment 22938

Furthermore this applies:

Attachment 22939

This I can't explain, if someone could explain to me why and how (detailed if possible), it would be great.

Sorry if it is obvius, but I'm new to this.

Thanks :)

Re: Help rewriting a differential equation

$\displaystyle \frac{d}{dx} (\frac{d\psi}{d\zeta} \frac{d\zeta}{dx})= (\frac{d}{dx}\frac{d\psi}{d\zeta}) \frac{d\zeta}{dx}+ (\frac{d}{dx}\frac{d\zeta}{dx}) \frac{d\psi}{d\zeta})=(\frac{d^2\psi}{d\zeta^2} \frac{d\zeta}{dx})\frac{d\zeta}{dx}+(\frac{d^2 \zeta }{dx^2}) \frac{d\psi}{d\zeta}$

Your expression misses the second term above.

By the way for the first equality your wrote it's just the chain rule, Chain rule - Wikipedia, the free encyclopedia

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Re: Help rewriting a differential equation

I'm not quite sure how you get that.. But i came up with this, bacause of what you wrote:

Attachment 22944

I think this is the solution? Is this properly written mathematically?

Re: Help rewriting a differential equation

I think you should also read about Leibniz product derivation formula, here:

Product rule - Wikipedia, the free encyclopedia

Re: Help rewriting a differential equation

Okay, Thanks, I'll look in to it..

- But is what I have done wrong? I'm just wondering, since i get the right result..