Differentation of Partial Derivative with respective to high order

[danong]

[SOLVED, THANKS]Differentation of Partial Derivative with respective to high order

hi there, i am actually studying about functional equation.
I got stucked with some derivatives problem,
and where i could find nowhere to refer or study from,
because it seems it is out of university book level.

my question is this :

what does it means by taking derivative with respect to partial derivative?
can anyone visualize this idea to me?
because i couldn't figure out the term with respect to partial derivative,
when it comes to a functional equation,
of which is a differential equations.

For e.g : F(x,y(x),y'(x),y''(x)) , find $$\frac{d}{dx}$$ of $$\partial$$ F(x,y(x),y'(x),y''(x)) / $$\partial$$ y' .

How can we write the full solution with partial derivative respect to y' ? and how bout y''?

 

[Cyosis]

Use the chain rule.

 

[danong]

for example?

 

[Cyosis]

How would you usually apply the chain rule for a function with multiple variables?

 

[danong]

sorry i couldn't understand, can you show me the way?
much appreciated.

 

[Cyosis]

You couldn't understand what exactly? Are you telling me that you don't know what the chain rule is?

 

[danong]

yeah, sort of, I'm not good in this, can u show me the general solution with respect to this particular problem?

Please ... if you know how, just show me the solution, don't try to test my skills, i am not good in this. that's why i need help.

Thanks in advance.

God Bless your day.

 

[Cyosis]

There really is no point in me giving you the answer when you don't know what the chain rule is.

I suggest you read http://en.wikipedia.org/wiki/Chain_rule.

 

[danong]

okay thanks for sharing,
now i fully understand the rule of this chain rule,
but still don't quite sure how to solve the problem stated above.

could you please provide the solution?


Thanks in advance.

God bless~

 

[Cyosis]

If you fully understand the chain rule now you should be able to make an attempt. Show us such an attempt so we can see where you get stuck.

 

[danong]

God bless, i solved it.

 

[berkeman]

Good job, Cyosis.

 

[danong]

yah ^^ he did a good job *thumbs up* =)
thanks for everything~

 

[danong]

This forum really need a lot of people like Cyosis, so that everyone who post questions eventually choose to answer themselves, cheers~ ^^