# Differentation of Partial Derivative with respective to high order

1. May 20, 2010

### 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''?

Last edited: May 20, 2010
2. May 20, 2010

### Cyosis

Use the chain rule.

3. May 20, 2010

### danong

for example?

4. May 20, 2010

### Cyosis

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

5. May 20, 2010

### danong

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

6. May 20, 2010

### Cyosis

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

7. May 20, 2010

### 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.

8. May 20, 2010

### Cyosis

9. May 20, 2010

### 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?

God bless~

10. May 20, 2010

### 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.

11. May 20, 2010

### danong

God bless, i solved it.

12. May 20, 2010

### Staff: Mentor

Good job, Cyosis.

13. May 21, 2010

### danong

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

14. May 21, 2010

### danong

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