Solving d/dx from dy/dx in Maths

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Hi all,

This is not strictly a DE question, but I came across this while working on one. This isn't the first time I got this and I just can't remember this from my 1st year maths. Some knowledge would be greatly appreciated. In the answer they do the following:

(\frac{1}{x})(\frac{dy}{dx}) - (\frac{1}{x^2})y \Rightarrow<br /> <br /> (\frac{d}{dx})[(\frac{1}{x})y]

Now I want to know how? I just can't simplify it. Silly question, but need the help!

Thanks
 
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Welcome to PF, htdIO! :smile:

Are you familiar with the chain rule?

It is: \frac d {dx} f(y(x)) = \frac {df} {dy} \frac {dy} {dx}

Do you know how to apply this?
 
Hi and thanks!

I do know it. Just not quite sure how I should be applying it here? I've scribbled quite a bit down here now, trying to combine this with the product rule. Or am I heading in the wrong direction?
 
Sorry, you're right. You need to apply the product rule.
Do you know how to apply it to: (\frac{d}{dx})[(\frac{1}{x})y(x)]?
 
Haha, aah thanks. I must be more tired than I thought...
I'm guessing the only way to 'see' this (like they did it), is by recognizing it and a bit of practice?
 
Hah, after all the practice I got, I thought you needed the chain rule!
So much for all that practice! :wink:
 
Halfway through I actually remembered the quotient rule, which should make it quicker ;) Anyway, thanks again for getting me on the right track!
 
Neh, the quotient rule is not quicker in this case.
But good you remembered it! :smile:
 
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