# Math Help - Partial derivatives of third order

1. ## Partial derivatives of third order

Hey guys and gals, newbie here, welcome everyone!

I need some help on solving the following problem: (see attached file).

Any help and hints are appreciated, thanks for reading!

2. Originally Posted by Iukwim
Hey guys and gals, newbie here, welcome everyone!

I need some help on solving the following problem: (see attached file).

Any help and hints are appreciated, thanks for reading!
Where exactly are you having trouble? Just take the partial derivatives and apply that combination, see if you get the RHS...

3. The only reasonable "hint" is "Do it!". Take those third derivatives and put then into the equation to see if it is satisfied.

Is your difficulty with the derivative? What do you get for the first and second derivatives?

Prove It got in ahead of me again! I need to type faster!

4. I was asking because the third derivatives looked terrible and I thought I might be missing some theorems or properties.

It turned out that the solution is rather simple than calculating directly.

The ln function can be represented as following:

And then computing is much easier (otherwise the third derivatives looked terrible).

Thanks for the encouragement, guys!